├── cover.jpg ├── errata.md ├── Lynch R2017b.zip ├── Lynch_R2020a.zip ├── Lynch R2016a ├── lena.jpg ├── Program_8d.mn ├── Simulink_1.slx ├── Simulink_2.slx ├── Simulink_3.slx ├── Programs_11f.mn ├── Programs_16b.mn ├── Simulink_10.slx ├── MMU_Mock_Exam_1.pdf ├── MMU_Mock_Exam_2.pdf ├── Programs_20b.m ├── Programs_15f.m ├── Programs_15fff.m ├── Programs_15ff.m ├── Programs_13a.m ├── Programs_20e.m ├── Program_3c.m ├── Programs_13b.m ├── Programs_16c.m ├── Programs_20c.m ├── Programs_13c.m ├── Program_2b.m ├── Program_6d.m ├── Program_8c.m ├── Program_8a.m ├── Programs_15c.m ├── Programs_15a.m ├── Program_1c.m ├── Program_6e.m ├── Programs_14a.m ├── Program_1d.m ├── Program_8e.m ├── Programs_14b.m ├── Program_8b.m ├── Program_3f.m ├── Programs_10a.m ├── Programs_12a.m ├── Programs_11a.m ├── Program_6a.m ├── Programs_20g.m ├── Programs_11c.m ├── Program_3g.m ├── Programs_10b.m ├── Programs_14c.m ├── Programs_15d.m ├── Programs_19c.m ├── Program_6f.m ├── Program_6b.m ├── Program_3e.m ├── Program_5a.m ├── Programs_18d.m ├── Program_3d.m ├── Program_5b.m ├── Program_2a.m ├── Programs_20h.m ├── Programs_11b.m ├── Programs_16d.m ├── Programs_19a.m ├── Program_7b.m ├── Programs_13d.m ├── Program_3b.m ├── Programs_12b.m ├── Program_9a.m ├── Programs_20d.m ├── Program_4a.m ├── Programs_14f.m ├── Programs_15e.m ├── Program_6c.m ├── Program_9b.m ├── Programs_19b.m ├── Program_4b.m ├── Programs_14e.m ├── Program_7c.m ├── Programs_11e.m ├── Programs_15g.m ├── Program_3a.m ├── Programs_15k.m ├── Programs_20f.m ├── Programs_15h.m ├── license.txt ├── Programs_16e.m ├── Programs_15b.m ├── Program_7a.m ├── Programs_18a.m ├── Programs_11d.m ├── Program_5c.m ├── Programs_16a.m ├── Program_5d.m ├── Program_4c.m ├── Programs_20a.m ├── Programs_18b.m ├── Programs_16f.m ├── Programs_18e.m ├── Program_1b.m ├── Program_1a.m ├── Programs_18c.m ├── Programs_14d.m ├── Index of MATLAB Files.txt └── housing.txt ├── Book Table of Contents.txt ├── Errata_DSAM_Chapter_11.pdf ├── README.md ├── contributing.md ├── LICENSE.txt └── Index of MATLAB Files.txt /cover.jpg: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/springer-math/Dynamical-Systems-with-Applications-using-MATLAB/HEAD/cover.jpg -------------------------------------------------------------------------------- /errata.md: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/springer-math/Dynamical-Systems-with-Applications-using-MATLAB/HEAD/errata.md -------------------------------------------------------------------------------- /Lynch R2017b.zip: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/springer-math/Dynamical-Systems-with-Applications-using-MATLAB/HEAD/Lynch R2017b.zip -------------------------------------------------------------------------------- /Lynch_R2020a.zip: 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-------------------------------------------------------------------------------- https://raw.githubusercontent.com/springer-math/Dynamical-Systems-with-Applications-using-MATLAB/HEAD/Lynch R2016a/MMU_Mock_Exam_2.pdf -------------------------------------------------------------------------------- /Lynch R2016a/Programs_20b.m: -------------------------------------------------------------------------------- 1 | % Programs 20b - Transfer function. 2 | % Chapter 20 - Binary Oscillator Computing. 3 | % Copyright Springer 2014. Stephen Lynch. 4 | % Binary oscillator half adder. 5 | % Run Programs_20d. 6 | 7 | function ans=Programs_20b(y,m,p); 8 | ans=1./(1+exp(m*y+p)); 9 | 10 | % End of Programs 20b. -------------------------------------------------------------------------------- /Lynch R2016a/Programs_15f.m: -------------------------------------------------------------------------------- 1 | % Programs 15f. Function file for Duffing system. 2 | % Chapter 15 - Poincare Maps and Nonautonomous Systems in the Plane. 3 | % Copyright Springer 2014. Stephen Lynch. 4 | % Run Programs_15g. 5 | 6 | function xdot=Programs_15f(t,x) 7 | % The Duffing System. 8 | global Gamma; 9 | xdot(1)=x(2); 10 | xdot(2)=x(1)-0.1*x(2)-(x(1))^3+Gamma*cos(1.25*t); 11 | xdot=[xdot(1);xdot(2)]; -------------------------------------------------------------------------------- /Lynch R2016a/Programs_15fff.m: -------------------------------------------------------------------------------- 1 | % Programs 15f. Function file for Duffing system. 2 | % Chapter 15 - Poincare Maps and Nonautonomous Systems in the Plane. 3 | % Copyright Springer 2014. Stephen Lynch. 4 | % Run Programs_15k. 5 | 6 | function xdot=Programs_15j(t,x) 7 | % The Duffing System. 8 | global Gamma; 9 | xdot(1)=x(2); 10 | xdot(2)=-x(1)-0.1*x(2)-0.1*(x(1))^3+Gamma*cos(1.25*t); 11 | xdot=[xdot(1);xdot(2)]; -------------------------------------------------------------------------------- /Lynch R2016a/Programs_15ff.m: -------------------------------------------------------------------------------- 1 | % Programs 15ff. Function file for Duffing system with k=0.3. 2 | % Chapter 15 - Poincare Maps and Nonautonomous Systems in the Plane. 3 | % Copyright Springer 2014. Stephen Lynch. 4 | % Run Programs_15h. 5 | 6 | function xdot=Programs_15ff(t,x) 7 | % The Duffing System. 8 | global Gamma; 9 | xdot(1)=x(2); 10 | xdot(2)=x(1)-0.3*x(2)-(x(1))^3+Gamma*cos(1.25*t); 11 | xdot=[xdot(1);xdot(2)]; -------------------------------------------------------------------------------- /Lynch R2016a/Programs_13a.m: -------------------------------------------------------------------------------- 1 | % Programs 13a - Animation of a Simple Curve. 2 | % Chapter 13 - Bifurcation Theory. 3 | % Copyright Springer 2014. Stephen Lynch. 4 | 5 | % The curve y=mu-x^2, for mu from -4 to +4. 6 | clear 7 | axis tight 8 | % Record the movie 9 | x=-4:.1:4; 10 | for n = 1:9 11 | plot(x,(n-5)-x.^2,x,0); 12 | M(n) = getframe; 13 | end 14 | % Use the movieviewer to watch the animation. 15 | movieview(M) 16 | 17 | % End of Programs 13a. -------------------------------------------------------------------------------- /Lynch R2016a/Programs_20e.m: -------------------------------------------------------------------------------- 1 | % Programs 20e - Josephson junction system. 2 | % Chapter 20 - Binary Oscillator Computing 3 | % Copyright Springer 2014. Stephen Lynch. 4 | % Run Programs 20f. 5 | % Make sure Programs 20f is in your directory. 6 | 7 | function xdot=Programs_20e(t,x) 8 | % The JJ system. 9 | % Run Programs_20f. 10 | global kappa; 11 | xdot(1)=x(2); 12 | xdot(2)=kappa-0.6*x(2)-sin(x(1)); 13 | xdot=[xdot(1);xdot(2)]; 14 | 15 | % End of Programs 20e. -------------------------------------------------------------------------------- /Lynch R2016a/Program_3c.m: -------------------------------------------------------------------------------- 1 | % Program 3c - Computing a Lyapunov Exponent for the Logistic Map. 2 | % Chapter 3 - Nonlinear Discrete Dynamical Systems. 3 | % Copyright Springer 2014. Stephen Lynch. 4 | 5 | % Lyapunov exponent when mu=4 (Table 3.1). 6 | clear; 7 | mu=4;x=0.1;xo=x; 8 | itermax=49999; 9 | for n=1:itermax 10 | xn=mu*xo*(1-xo); 11 | x=[x xn]; 12 | xo=xn; 13 | end 14 | 15 | Liap_exp=vpa(sum(log(abs(mu*(1-2*x))))/itermax,6) 16 | 17 | % End of Program 3c. 18 | -------------------------------------------------------------------------------- /Lynch R2016a/Programs_13b.m: -------------------------------------------------------------------------------- 1 | % Programs 13b - Finding critical points and bifurcation curve. 2 | % Chapter 13 - Bifurcation Theory. 3 | % Copyright Springer 2014. Stephen Lynch. 4 | 5 | % Critical points for y=mu*x-x^3. 6 | % Symbolic Math toolbox required. 7 | syms x y 8 | [x,y]=solve('mu*x-x^3','-y') 9 | 10 | % Plot a simple bifurcation diagram (Fig. 13.11). 11 | r=0:.01:2; 12 | mu=.28*r.^6-r.^4+r.^2; 13 | plot(mu,r) 14 | fsize=15; 15 | xlabel('\mu','Fontsize',fsize); 16 | ylabel('r','Fontsize',fsize); 17 | 18 | % End Programs 13b. -------------------------------------------------------------------------------- /Lynch R2016a/Programs_16c.m: -------------------------------------------------------------------------------- 1 | % Programs 16c - Hopf Bifurcation. Function file. 2 | % Chapter 16 - Bifurcations of Nonlinear Systems in the Plane. 3 | % Copyright Springer 2014. Stephen Lynch. 4 | 5 | % Animation of Hopf bifurcation of a limit cycle from the origin. 6 | % NOTE: Run Programs 16d NOT Programs 16c. 7 | 8 | function sys=Programs_16c(~,x) 9 | global mu 10 | X=x(1,:); 11 | Y=x(2,:); 12 | % Define the system. 13 | P=Y+10.*X.*(0.1-Y.^2); 14 | Q=-X+mu; 15 | 16 | sys=[P;Q]; 17 | 18 | % End of Programs 16c. 19 | 20 | -------------------------------------------------------------------------------- /Lynch R2016a/Programs_20c.m: -------------------------------------------------------------------------------- 1 | % Programs 20c - Fitzhugh Nagumo Binary Oscillator Half-Adder. 2 | % Run Programs 20d. 3 | 4 | function cols=Programs_20c(t,y,pars,I,mat,noise,m,p); 5 | a=pars(1);b=pars(2);c=pars(3); 6 | mat=mat'; 7 | nodes=floor(length(y)/2); 8 | cols=zeros(nodes*2,1); 9 | u=y(1:2:end); 10 | v=y(2:2:end); 11 | cols(1:2:end)=-u.*(u-a).*(u-1)-v+I; 12 | cols(2:2:end)=c*(u-b*v); 13 | cols(1:2:end)=cols(1:2:end)+mat*Programs_20b(v,m,p); 14 | cols=cols+randn(length(cols),1)*noise; 15 | return; 16 | 17 | % End of Programs 20c. 18 | -------------------------------------------------------------------------------- /Lynch R2016a/Programs_13c.m: -------------------------------------------------------------------------------- 1 | % Programs 13c - Hopf Bifurcation. Function file. 2 | % Chapter 13 - Bifurcations of Nonlinear Systems in the Plane. 3 | % Copyright Springer 2014. Stephen Lynch. 4 | 5 | % Animation of Hopf bifurcation of a limit cycle from the origin. 6 | % NOTE: Run Programs_13d NOT Programs_13c. 7 | 8 | function sys=Programs_13c(~,x) 9 | global mu 10 | X=x(1,:); 11 | Y=x(2,:); 12 | 13 | % Define the system. 14 | P=Y+mu*X-X.*Y.^2; 15 | Q=mu*Y-X-Y.^3; 16 | 17 | sys=[P;Q]; 18 | % End of Programs 13c. 19 | 20 | -------------------------------------------------------------------------------- /Lynch R2016a/Program_2b.m: -------------------------------------------------------------------------------- 1 | % Program 2b - The Leslie Matrix. 2 | % Chapter 2 - Linear Discrete Dynamical Systems. 3 | % Copyright Springer 2014. Stephen Lynch. 4 | % Commands are short enough for the Command Window. 5 | 6 | % Define a 3x3 Leslie Matrix (Example 4). 7 | L=[0 3 1; 0.3 0 0; 0 0.5 0] 8 | 9 | % Set initial conditions. 10 | X0=[1000;2000;3000] 11 | 12 | % After 10 years the population distribution will be: 13 | X10=L^10*X0 14 | 15 | % Find the eigenvectors and eigenvalues of L (Example 5). 16 | [v,d]=eig(L) 17 | 18 | % End of Program 2b. -------------------------------------------------------------------------------- /Lynch R2016a/Program_6d.m: -------------------------------------------------------------------------------- 1 | % Program_6d - The tau curve. 2 | % Chapter 6 - Fractals and Multifractals. 3 | % Copyright Springer 2014. Stephen Lynch. 4 | 5 | % Plot a tau curve for a multifractal Cantor set (Figure 6.16a). 6 | ezplot('(log((1/9)^x+(8/9)^x))/(log(3))',[-20,20]) 7 | axis([-20 20 -8 20]) 8 | fsize=15; 9 | set(gca,'XTick',-20:10:20,'FontSize',fsize) 10 | set(gca,'YTick',-8:4:20,'FontSize',fsize) 11 | xlabel('\itq','FontSize',fsize) 12 | ylabel('\it{\tau(q)}','FontSize',fsize) 13 | title(' ') 14 | 15 | % End of Program_6d. 16 | 17 | 18 | -------------------------------------------------------------------------------- /Lynch R2016a/Program_8c.m: -------------------------------------------------------------------------------- 1 | % Program 8c - Solving Simple Differential Equations. 2 | % Chapter 8 - Differential Equations. 3 | % Copyright Springer 2014. Stephen Lynch. 4 | 5 | % Chemical kinetics (Example 8, Figure 8.7). 6 | k=0.00713; 7 | deqn = @(t,c) k*(4-c)^2*(1-c/2); 8 | [t,ca]=ode45(deqn,[0 400],0); 9 | plot(t,ca(:,1)) 10 | axis([0 400 0 3]) 11 | fsize=15; 12 | set(gca,'XTick',0:100:400,'FontSize',fsize) 13 | set(gca,'YTick',0:1:3,'FontSize',fsize) 14 | xlabel('t','FontSize',fsize) 15 | ylabel('c(t)','FontSize',fsize) 16 | hold off 17 | 18 | % End of Program 8c. -------------------------------------------------------------------------------- /Lynch R2016a/Program_8a.m: -------------------------------------------------------------------------------- 1 | % Program 8a - Solving Simple Differential Equations. 2 | % Chapter 8 - Differential Equations. 3 | % Symbolic Math toolbox required. 4 | % Copyright Springer 2014. Stephen Lynch. 5 | 6 | % A separable ODE (Example 1). 7 | soln1=dsolve('Dx=-t/x') 8 | 9 | % Chemical kinetics (Example 8). 10 | a=4;b=1;k=.00713; 11 | soln2=dsolve('Dc=k*(a-c)^2*(b-c/2)') 12 | % Implicit solution is returned. 13 | 14 | % A 3-D system (Exercise 7). 15 | w=dsolve('Dx=-a*x','Dy=a*x-b*y','Dz=b*y'); 16 | xsol=w.x 17 | ysol=w.y 18 | zsol=w.z 19 | 20 | % End of Program 8a. -------------------------------------------------------------------------------- /Lynch R2016a/Programs_15c.m: -------------------------------------------------------------------------------- 1 | % Programs 15c - Phase portraits for nonautonomous systems. 2 | % Chapter 15 - Poincare Maps and Nonautonomous Systems in the Plane. 3 | % Copyright Springer 2014. Stephen Lynch. 4 | 5 | % Phase portrait for the Duffing system. 6 | 7 | deq=@(t,x) [x(2);x(1)-0.3*x(2)-(x(1))^3+0.5*cos(1.25*t)]; 8 | options=odeset('RelTol',1e-4,'AbsTol',1e-4); 9 | [t,xx]=ode45(deq,[0 200],[1,0],options); 10 | 11 | plot(xx(:,1),xx(:,2)) 12 | 13 | fsize=15; 14 | axis([-2 2 -2 2]) 15 | xlabel('x','FontSize',fsize) 16 | ylabel('y','FontSize',fsize) 17 | 18 | % End of Programs 15c. -------------------------------------------------------------------------------- /Lynch R2016a/Programs_15a.m: -------------------------------------------------------------------------------- 1 | % Programs 15a - Solving an initial value problem. 2 | % Chapter 15 - Poincare Maps and Nonautonomous Systems in the Plane. 3 | % Copyright Springer 2014. Stephen Lynch. 4 | 5 | % Solve a differential equation (Example 1). 6 | r=dsolve('Dr=-r^2','r(0)=1'); 7 | 8 | % List the first eight returns on the segment {y=0, 060 % Switch on the control when n>60. 14 | x(n+1)=k*mu*x(n)*(1-x(n)); % Nudge the system every second iterate. 15 | x(n+2)=mu*x(n+1)*(1-x(n+1)); 16 | end 17 | end 18 | hold on 19 | plot(1:itermax,x(1:itermax)) 20 | plot(1:itermax,x(1:itermax),'o') 21 | fsize=15; 22 | set(gca,'XTick',0:50:itermax,'FontSize',fsize) 23 | set(gca,'YTick',[0,1],'FontSize',fsize) 24 | xlabel('n','FontSize',fsize) 25 | ylabel('\itx_n','FontSize',fsize) 26 | hold off 27 | 28 | % End of Program 19a. -------------------------------------------------------------------------------- /Lynch R2016a/Program_7b.m: -------------------------------------------------------------------------------- 1 | % Program 7b - Chaotic attractor and power spectrum. 2 | % Chapter 7 - Image Processing. 3 | % Copyright Springer 2014. Stephen Lynch. 4 | 5 | a=1;b=0.3; 6 | N=100000;x=zeros(1,N);y=zeros(1,N); 7 | x(1)=0.1;y(1)=0.1; 8 | for n=1:N 9 | x(n+1)=1-a*(y(n))^2+b*x(n); 10 | y(n+1)=x(n); 11 | end 12 | subplot(2,1,1); 13 | plot(x(10:N),y(10:N),'.','MarkerSize',1); 14 | fsize=15;axis([-1 2 -1 2]); 15 | set(gca,'XTick',-1:1:2,'FontSize',fsize) 16 | set(gca,'YTick',-1:1:2,'FontSize',fsize) 17 | xlabel('x','FontSize',fsize) 18 | ylabel('y','FontSize',fsize) 19 | 20 | % Power spectrum (Figure 7.5(f)). 21 | f=-N/2+1:N/2; 22 | freq=f*2/N; 23 | Pow=abs(fft(x,N).^2); 24 | subplot(2,1,2); 25 | plot(freq,log(Pow)); 26 | Pmax=20;axis([0 1 -10 Pmax]); 27 | set(gca,'XTick',0:0.5:1,'FontSize',fsize) 28 | set(gca,'YTick',-10:5:20,'FontSize',fsize) 29 | xlabel('Frequency (Hz)'); 30 | ylabel('log(Power)'); 31 | 32 | % End of Program 7b. -------------------------------------------------------------------------------- /Lynch R2016a/Programs_13d.m: -------------------------------------------------------------------------------- 1 | % Programs 13d - Hopf Bifurcation movie. 2 | % Chapter 13 - Bifurcations of Nonlinear Systems in the Plane. 3 | % Copyright Springer 2014. Stephen Lynch. 4 | 5 | % Animation of Hopf bifurcation of a limit cycle from the origin. 6 | % NOTE: Programs_13c must be in the same directory as Programs_13d. 7 | clear 8 | global mu 9 | for j = 1:48 10 | F(j) = getframe; 11 | mu=j/40-1; % mu goes from -1 to 0.2. 12 | options = odeset('RelTol',1e-4,'AbsTol',1e-4); 13 | x0=0.5;y0=0.5; 14 | [t,x]=ode45(@Programs_13c,[0 80],[x0 y0],options); 15 | plot(x(:,1),x(:,2),'b'); 16 | axis([-1 1 -1 1]) 17 | fsize=15; 18 | set(gca,'XTick',-1:0.2:1,'FontSize',fsize) 19 | set(gca,'YTick',-1:0.2:1,'FontSize',fsize) 20 | xlabel('x(t)','FontSize',fsize) 21 | ylabel('y(t)','FontSize',fsize) 22 | title('Hopf Bifurcation','FontSize',15); 23 | 24 | F(j) = getframe; 25 | 26 | end 27 | 28 | movie(F,5) 29 | 30 | % End of Programs 13d. 31 | 32 | -------------------------------------------------------------------------------- /Lynch R2016a/Program_3b.m: -------------------------------------------------------------------------------- 1 | % Program 3b - Graphical Iteration of the Logistic Map. 2 | % Chapter 3 - Nonlinear Discrete Dynamical Systems. 3 | % Copyright Springer 2014. Stephen Lynch. 4 | 5 | clear; 6 | figure; 7 | fsize=15; 8 | nmax=100;halfm=nmax/2; 9 | t=zeros(1,nmax);t1=zeros(1,nmax);t2=zeros(1,nmax); 10 | t(1)=0.2; 11 | mu=3.8282; 12 | axis([0 1 0 1]); 13 | for n=1:nmax 14 | t(n+1)=mu*t(n)*(1-t(n)); 15 | end 16 | 17 | for n=1:halfm 18 | t1(2*n-1)=t(n); 19 | t1(2*n)=t(n); 20 | end 21 | 22 | t2(1)=0;t2(2)=t(2); 23 | for n=2:halfm 24 | t2(2*n-1)=t(n); 25 | t2(2*n)=t(n+1); 26 | end 27 | hold on 28 | plot(t1,t2,'r'); 29 | fplot('3.8282*x*(1-x)',[0 1]); 30 | x=[0 1];y=[0 1]; 31 | plot(x,y,'g'); 32 | hold off 33 | %title('Graphical iteration for the tent map') 34 | set(gca,'xtick',[0 1],'Fontsize',fsize) 35 | set(gca,'ytick',[0 1],'Fontsize',fsize) 36 | xlabel('x','Fontsize',fsize) 37 | ylabel('f_{\mu}','Fontsize',fsize) 38 | 39 | % End of Program 3b. 40 | -------------------------------------------------------------------------------- /Lynch R2016a/Programs_12b.m: -------------------------------------------------------------------------------- 1 | % Programs 12b: Lyapunov function for a Hopfield network. 2 | % Chapter 12 - Hamiltonian Systems, Lyapunov Functions, and Stability. 3 | % Copyright Springer 2014. Stephen Lynch. 4 | % See Figure 12.8(a) and (b). 5 | 6 | figure 7 | fsize=15; 8 | ezsurf('-(x^2+y^2)-4*(log(cos(pi*x/2))+log(cos(pi*y/2)))/(0.7*pi^2)',[-1,1,-1,1]); 9 | title('Surface plot','FontSize',fsize) 10 | axis([-1 1 -1 1 -0.5 1]) 11 | set(gca,'XTick',-1:0.5:1,'FontSize',fsize) 12 | set(gca,'YTick',-1:0.5:1,'FontSize',fsize) 13 | xlabel('a_1','FontSize',fsize) 14 | ylabel('a_2','FontSize',fsize) 15 | 16 | figure 17 | x=-1:.01:1;y=-1:.01:1;[X,Y]=meshgrid(x,y); 18 | Z=-(X.^2+Y.^2)-4*(log(cos(pi*X/2))+log(cos(pi*Y/2)))./(0.7*pi^2); 19 | contour(X,Y,Z,-1:.01:1) 20 | title('Contour plot','FontSize',fsize) 21 | set(gca,'XTick',-1:0.5:1,'FontSize',fsize) 22 | set(gca,'YTick',-1:0.5:1,'FontSize',fsize) 23 | xlabel('a_1','FontSize',fsize) 24 | ylabel('a_2','FontSize',fsize) 25 | 26 | % End of Programs 12b. -------------------------------------------------------------------------------- /Lynch R2016a/Program_9a.m: -------------------------------------------------------------------------------- 1 | % Program 9a - Phase Portrait (Fig. 9.8(a)). 2 | % Chapter 9 - Planar Systems. 3 | % Copyright Springer 2014. Stephen Lynch. 4 | 5 | % Phase portrait of a linear system of ODE's. 6 | % IMPORTANT - vectorfield.m must be in same directory. 7 | clear;figure; 8 | sys = @(t,x) [2*x(1)+x(2);x(1)+2*x(2)]; 9 | vectorfield(sys,-3:.25:3,-3:.25:3) 10 | hold on 11 | for x0=-3:1.5:3 12 | for y0=-3:1.5:3 13 | [ts,xs] = ode45(sys,[0 5],[x0 y0]); 14 | plot(xs(:,1),xs(:,2)) 15 | end 16 | end 17 | for x0=-3:1.5:3 18 | for y0=-3:1.5:3 19 | [ts,xs] = ode45(sys,[0 -5],[x0 y0]); 20 | plot(xs(:,1),xs(:,2)) 21 | end 22 | end 23 | hold off 24 | axis([-3 3 -3 3]) 25 | fsize=15; 26 | set(gca,'XTick',-3:1:3,'FontSize',fsize) 27 | set(gca,'YTick',-3:1:3,'FontSize',fsize) 28 | xlabel('x(t)','FontSize',fsize) 29 | ylabel('y(t)','FontSize',fsize) 30 | hold off 31 | 32 | % End of Program 9a. -------------------------------------------------------------------------------- /Lynch R2016a/Programs_20d.m: -------------------------------------------------------------------------------- 1 | % Programs 20d - Binary oscillator half adder. 2 | % Chapter 20 - Binary Oscillator Computing. 3 | % Copyright Springer 2014. Stephen Lynch. 4 | % Ensure Programs 20b and 20c are in the same directory. 5 | % See Figure 20.5(b). 6 | 7 | clear; 8 | tmax=500; 9 | tspan=[0 tmax]; 10 | e1=0.8; e2=0.45; i1=-1.5; 11 | mat=[0 0 e1 e2 12 | 0 0 e1 e2 13 | 0 0 0 0 14 | 0 0 i1 0] 15 | I=[0 0 0 0 16 | 0 1 0 0 17 | 1 0 0 0 18 | 1 1 0 0]; 19 | str=1; 20 | I=I*str; 21 | m=-100; p=60; 22 | yinit=zeros(size(mat,1)*2,1); 23 | a=0.1; b=0.1; c=0.1; 24 | noise=0; 25 | nodes=size(I,2); 26 | ylong=[];tlong=[]; 27 | for loop1=1:size(I,1) 28 | [t,y]=ode45(@Programs_20c,tspan,yinit,[],[a b c],I(loop1,:)',mat,noise,m,p); 29 | yinit=y(end,:)'; 30 | tlong=[tlong;t+(loop1-1)*tmax]; 31 | ylong=[ylong;y]; 32 | end 33 | figure(1) 34 | for loop=1:nodes 35 | subplot(nodes,1,loop) 36 | plot(tlong,ylong(:,2*loop-1)) 37 | axis([tlong(1) tlong(end) -1 1.5]) 38 | end 39 | 40 | % End of Pragrams 20d. 41 | -------------------------------------------------------------------------------- /Lynch R2016a/Program_4a.m: -------------------------------------------------------------------------------- 1 | % Program 4a - Julia Sets. 2 | % Chapter 4 - Complex Iterative Maps. 3 | % Copyright Springer 2014. Stephen Lynch. 4 | 5 | % Plot the Julia set J(0,1.1) (Figure 4.1(d)). 6 | clear 7 | figure 8 | k=20;niter=2^k; 9 | x=zeros(1,niter);y=zeros(1,niter); 10 | x1=zeros(1,niter);y1=zeros(1,niter); 11 | a=0;b=1.1; 12 | x(1)=real(0.5+sqrt(0.25-(a+1i*b))); 13 | y(1)=imag(0.5+sqrt(0.25-(a+1i*b))); 14 | % Check that the point is unstable. 15 | isunstable=2*abs(x(1)+1i*y(1)); 16 | 17 | hold on 18 | for n=1:niter 19 | x1=x(n);y1=y(n); 20 | u=sqrt((x1-a)^2+(y1-b)^2)/2;v=(x1-a)/2; 21 | u1=sqrt(u+v);v1=sqrt(u-v); 22 | x(n+1)=u1;y(n+1)=v1; 23 | if y(n)198 % Check point is in control region. 15 | x(n+1)=(-k1*(x(n)-xstar)-k2*(y(n)-ystar)+alpha)+beta*y(n)-(x(n))^2; 16 | y(n+1)=x(n); 17 | else 18 | x(n+1)=alpha+beta*y(n)-(x(n))^2; 19 | y(n+1)=x(n); 20 | end 21 | rsqr(n+1)=(x(n+1))^2+(y(n+1))^2; 22 | end 23 | hold on 24 | axis([0 N 0 6]) 25 | plot(1:N,rsqr(1:N)) 26 | plot(1:N,rsqr(1:N),'o') 27 | fsize=15; 28 | set(gca,'XTick',0:50:N,'FontSize',fsize) 29 | set(gca,'ytick',[0,6],'FontSize',fsize) 30 | xlabel('n','FontSize',fsize) 31 | ylabel('\it{r^2}','FontSize',fsize) 32 | hold off 33 | 34 | % End of Program 19b. -------------------------------------------------------------------------------- /Lynch R2016a/Program_4b.m: -------------------------------------------------------------------------------- 1 | % Program 4b - The Black and White Mandelbrot Set. 2 | % Chapter 4 - Complex Iterative Maps. 3 | % Thanks to Steve Lord from The MathWorks for his help. 4 | % Copyright Springer 2014. Stephen Lynch. 5 | 6 | % Vectorized program. 7 | % Plot the Mandelbrot set in black and white (Figure 4.2). 8 | Nmax = 50; scale = 0.005; 9 | xmin = -2.4; xmax = 1.2; 10 | ymin = -1.5; ymax = 1.5; 11 | 12 | % Generate x and y coordinates and z complex values 13 | [x,y]=meshgrid(xmin:scale:xmax,ymin:scale:ymax); 14 | z = x+1i*y; 15 | 16 | % Generate w accumulation matrix and k counting matrix 17 | w = zeros(size(z)); 18 | k = zeros(size(z)); 19 | 20 | N = 0; 21 | while N4) = N; 25 | end 26 | k(k==0) = Nmax; 27 | figure 28 | s = pcolor(x, y, mod(k, 2)); 29 | colormap([0 0 0;1 1 1]) 30 | set(s,'edgecolor','none') 31 | 32 | axis([xmin xmax -ymax ymax]) 33 | fsize=15; 34 | set(gca,'XTick',xmin:0.4:xmax,'FontSize',fsize) 35 | set(gca,'YTick',-ymax:0.5:ymax,'FontSize',fsize) 36 | xlabel('Re z','FontSize',fsize) 37 | ylabel('Im z','FontSize',fsize) 38 | 39 | % End of Program 4b -------------------------------------------------------------------------------- /Lynch R2016a/Programs_14e.m: -------------------------------------------------------------------------------- 1 | % Programs 14e - Time series of Belousov-Zhabotinski reaction. 2 | % Chapter 14 - Three-Dimensional Autonomous Systems and Chaos. 3 | % See URL: http://online.redwoods.edu/INSTRUCT/darnold/DEProj/Sp98/Gabe/bzreact.htm 4 | % Copyright Springer 2014. Stephen Lynch. 5 | 6 | fsize=15; 7 | A=0.06;B=0.02;f=1; 8 | k1=1.28;k2=2.4e6;k3=33.6;k4=3e3;kc=1; 9 | epsilon=(kc*B)/(k3*A); 10 | epsilondash=(2*kc*k4*B)/(k2*k3*A); 11 | q=(2*k1*k4*B)/(k2*k3*A); 12 | BZReaction=@(t,x) [(q*x(2)-x(1)*x(2)+x(1)*(1-x(1)))/epsilon;(-q*x(2)-x(1)*x(2)+f*x(3))/epsilondash;x(1)-x(3)]; 13 | options = odeset('RelTol',1e-6,'AbsTol',1e-6); 14 | [t,xa]=ode23s(BZReaction,[0 50],[0,0,0.1],options); 15 | subplot(3,1,1) 16 | plot(t,xa(:,1)) 17 | title('Relative concentration of bromous acid','Fontsize',fsize) 18 | xlabel('t','Fontsize',fsize); 19 | ylabel('x(t)','Fontsize',fsize); 20 | subplot(3,1,2) 21 | plot(t,xa(:,2),'r') 22 | title('Relative concentration of bromide ions','Fontsize',fsize) 23 | xlabel('t','Fontsize',fsize); 24 | ylabel('y(t)','Fontsize',fsize); 25 | subplot(3,1,3) 26 | plot(t,xa(:,3),'m') 27 | title('Relative concentration of cerium ions','Fontsize',fsize) 28 | xlabel('t','Fontsize',fsize); 29 | ylabel('z(t)','Fontsize',fsize); 30 | 31 | % End of Programs 14e. 32 | 33 | -------------------------------------------------------------------------------- /Lynch R2016a/Program_7c.m: -------------------------------------------------------------------------------- 1 | % Program 7c - Low pass filter on Lena.jpg. 2 | % Chapter 7 - Image Processing. 3 | % Ensure that lena.jpg is in the same directory. 4 | % Figure 7.6. 5 | % Copyright Springer 2014. Stephen Lynch. 6 | 7 | input_lena = double(rgb2gray(imread('lena.jpg'))); 8 | % First the processing 9 | fft_lena = fft2(input_lena); 10 | % This bit builds an idea lowpass filter. 11 | u = 0:(size(fft_lena,1)-1); 12 | v = 0:(size(fft_lena,2)-1); 13 | idx = find(u > size(fft_lena,1)/2); 14 | u(idx) = u(idx)-size(fft_lena,1); 15 | idy = find(v > size(fft_lena,2)/2); 16 | v(idy) = v(idy)-size(fft_lena,2); 17 | [V,U] = meshgrid(v,u); 18 | D = sqrt(U.^2 + V.^2); 19 | % The only parameter - 50 is the highest freqency allowed through. 20 | filter = double(D <= 50); 21 | fft_lena_blurr = fft_lena.*filter; 22 | lena_blurred = ifft2(fft_lena_blurr); 23 | % The images. 24 | lena_baa = [input_lena lena_blurred]; 25 | lena_baa = 255*mat2gray(lena_baa); 26 | fft_lena_abs = log(abs(fftshift(fft_lena))); 27 | fft_lena_blurr_abs = log(abs(fftshift(fft_lena_blurr))); 28 | lena_ffts = [fft_lena_abs fft_lena_blurr_abs]; 29 | lena_ffts(lena_ffts==-Inf) = 0; 30 | lena_ffts = 255*mat2gray(lena_ffts); 31 | lena_combined = [lena_baa ; lena_ffts]; 32 | figure; 33 | imagesc(lena_combined); axis image; colormap gray; axis off; 34 | 35 | % End of Program 7c. -------------------------------------------------------------------------------- /Lynch R2016a/Programs_11e.m: -------------------------------------------------------------------------------- 1 | % Programs 11e - Perturbation Methods 2 | % Chapter 11 - Limit Cycles. 3 | % Copyright Springer 2014. Stephen Lynch. 4 | 5 | % See Example 7. Apologies - there is an error in the book. 6 | % Solve the Order epsilon ODE. 7 | deq1=dsolve('D2x+x=cos(t)^3','x(0)=0','Dx(0)=0') 8 | O_epsilon=simplify(deq1) 9 | 10 | % Numerical solution of the Duffing equation. 11 | epsilon=0.01; 12 | deq2=@(t,x) [x(2);-x(1)+epsilon*x(1)^3]; 13 | [t,xa]=ode23s(deq2,[0,100],[1,0]); 14 | 15 | % Plot x_N-x_0: see Figure 11.9. 16 | subplot(2,1,1) 17 | plot(t,xa(:,1)-cos(t)) 18 | title('Duffing equation, one term expansion error: x_N-x_0','FontSize',fsize) 19 | ylim=0.5; 20 | axis([0 100 -ylim ylim]) 21 | fsize=15; 22 | set(gca,'XTick',0:10:100,'FontSize',fsize) 23 | set(gca,'YTick',-ylim:0.2:ylim,'FontSize',fsize) 24 | xlabel('x(t)','FontSize',fsize) 25 | ylabel('y(t)','FontSize',fsize) 26 | subplot(2,1,2) 27 | plot(t,xa(:,1)-cos(t)-epsilon*(cos(t)/8 - cos(t).^3/8 + (3*t.*sin(t))/8)) 28 | title('Duffing equation, two term expansion error: x_N-x_P','FontSize',fsize) 29 | ylim=0.18; 30 | axis([0 100 -ylim ylim]) 31 | fsize=15; 32 | set(gca,'XTick',0:10:100,'FontSize',fsize) 33 | set(gca,'YTick',-ylim:0.09:ylim,'FontSize',fsize) 34 | xlabel('x(t)','FontSize',fsize) 35 | ylabel('y(t)','FontSize',fsize) 36 | 37 | % End of Programs 11e. -------------------------------------------------------------------------------- /Lynch R2016a/Programs_15g.m: -------------------------------------------------------------------------------- 1 | % Programs 15g - Bifurcation diagram for the Duffing equation. 2 | % Chapter 15 - Poincare Maps and Nonautonomous Systems in the Plane. 3 | % Copyright Springer 2014. Stephen Lynch. 4 | 5 | % Make sure Programs 15f is in your directory. 6 | % This models a beam oscillating between two magnets. 7 | % Please see: E. Ott, Chaos in Dynamical Systems (2nd edition), 8 | % Cambridge University Press, 2002. 9 | clear 10 | global Gamma; 11 | Max=120;step=0.001;interval=Max*step;a=1;b=0; 12 | % Ramp the amplitude up. 13 | for n=1:Max 14 | Gamma=step*n; 15 | [t,x]=ode45('Programs_15f',0:(2*pi/1.25):(4*pi/1.25),[a,b]); 16 | a=x(2,1); 17 | b=x(2,2); 18 | rup(n)=sqrt((x(2,1))^2+(x(2,2))^2); 19 | end 20 | % Ramp the amplitude down. 21 | for n=1:Max 22 | Gamma=interval-step*n; 23 | [t,x]=ode45('Programs_15f',0:(2*pi/1.25):(4*pi/1.25),[a,b]); 24 | a=x(2,1); 25 | b=x(2,2); 26 | rdown(n)=sqrt((x(2,1))^2+(x(2,2))^2); 27 | end 28 | hold on 29 | rr=step:step:interval; 30 | plot(rr,rup) % Ramp up in blue. 31 | plot(interval-rr,rdown,'r') % Ramp down in red. 32 | hold off 33 | fsize=15; 34 | axis([0 .12 0 2]) 35 | xlabel('\Gamma','FontSize',fsize) 36 | ylabel('r','FontSize',fsize) 37 | title('Bistable Loop Duffing System','FontSize',fsize) 38 | 39 | % End of Programs 15g. -------------------------------------------------------------------------------- /Lynch R2016a/Program_3a.m: -------------------------------------------------------------------------------- 1 | % Program 3a - Graphical Iteration of the Ten Map. 2 | % Chapter 3 - Nonlinear Discrete Dynamical Systems. 3 | % Copyright Springer 2014. Stephen Lynch. 4 | 5 | % Program 3a: Graphical iteration. 6 | % Figure 3.7(b): The tent map. 7 | clear 8 | % Initial condition 0.2001, must be symbolic. 9 | nmax=200; 10 | t=sym(zeros(1,nmax));t1=sym(zeros(1,nmax));t2=sym(zeros(1,nmax)); 11 | t(1)=sym(2001/10000); 12 | mu=2; 13 | halfm=nmax/2; 14 | axis([0 1 0 1]); 15 | for n=2:nmax 16 | if (double(t(n-1)))>=0 && (double(t(n-1)))<=1/2 17 | t(n)=sym(2*t(n-1)); 18 | else 19 | if (double(t(n-1)))<=1 20 | t(n)=sym(2*(1-t(n-1))); 21 | end 22 | end 23 | end 24 | for n=1:halfm 25 | t1(2*n-1)=t(n); 26 | t1(2*n)=t(n); 27 | end 28 | t2(1)=0;t2(2)=double(t(2)); 29 | for n=2:halfm 30 | t2(2*n-1)=double(t(n)); 31 | t2(2*n)=double(t(n+1)); 32 | end 33 | hold on 34 | fsize=20; 35 | plot(double(t1),double(t2),'r'); 36 | x=[0 0.5 1];y=[0 mu/2 0]; 37 | plot(x,y,'b'); 38 | x=[0 1];y=[0 1]; 39 | plot(x,y,'g'); 40 | title('Graphical iteration for the tent map','FontSize',fsize) 41 | set(gca,'XTick',0:0.2:1,'FontSize',fsize) 42 | set(gca,'YTick',0:0.2:1,'FontSize',fsize) 43 | xlabel('x','FontSize',fsize) 44 | ylabel('T','FontSize',fsize) 45 | hold off 46 | 47 | % End of Program 3a. -------------------------------------------------------------------------------- /Lynch R2016a/Programs_15k.m: -------------------------------------------------------------------------------- 1 | % Programs 15k - Bifurcation diagram for the Duffing equation. 2 | % Chapter 15 - Poincare Maps and Nonautonomous Systems in the Plane. 3 | % Copyright Springer 2014. Stephen Lynch. 4 | 5 | % Make sure Programs 15fff is in your directory. 6 | % This models the nonlinear pendulum depicted in Figure 15.8. 7 | clear 8 | global Gamma; 9 | Max=100;step=0.01;interval=Max*step;a=0.01;b=0; 10 | % Ramp the amplitude up. 11 | for n=1:Max 12 | Gamma=step*n; 13 | [t,x]=ode23s('Programs_15fff',0:(2*pi/1.25):(4*pi/1.25),[a,b]); 14 | a=x(2,1); 15 | b=x(2,2); 16 | rup(n)=sqrt((x(2,1))^2+(x(2,2))^2); 17 | end 18 | % Ramp the amplitude down. 19 | for n=1:Max 20 | Gamma=interval-step*n; 21 | [t,x]=ode23s('Programs_15fff',0:(2*pi/1.25):(4*pi/1.25),[a,b]); 22 | a=x(2,1); 23 | b=x(2,2); 24 | rdown(n)=sqrt((x(2,1))^2+(x(2,2))^2); 25 | end 26 | hold on 27 | rr=step:step:interval; 28 | plot(rr,rup,'b','Linewidth',5) % Ramp up in blue. 29 | plot(interval-rr,rdown,'r','Linewidth',2) % Ramp down in red. 30 | hold off 31 | fsize=15; 32 | axis([0 1 0 5]) 33 | set(gca,'XTick',0:0.2:1,'FontSize',fsize) 34 | set(gca,'YTick',0:1:5,'FontSize',fsize) 35 | xlabel('\Gamma','FontSize',fsize) 36 | ylabel('r','FontSize',fsize) 37 | %title('Bistable Loop Duffing System','FontSize',fsize) 38 | -------------------------------------------------------------------------------- /Lynch R2016a/Programs_20f.m: -------------------------------------------------------------------------------- 1 | % Programs 20f - Bifurcation diagram for a Josephson Junction. 2 | % Chapter 20 - Binary Oscillator Computing 3 | % Copyright Springer 2014. Stephen Lynch. 4 | 5 | % Make sure Programs 20e is in your directory. 6 | clear 7 | figure 8 | global kappa;a=0;b=0;mins=120; 9 | Max=400;step=0.005;interval=Max*step;tmax=160; 10 | % Ramp kappa up. 11 | for n=1:Max 12 | kappa=step*n; 13 | options=odeset('RelTol',1e-4,'AbsTol',1e-4); 14 | [t,x]=ode45('Programs_20e',[0 tmax],[a,b],options); 15 | s=size(x(:,1),1); 16 | a=0;b=x(s,2); 17 | kappaup(n)=0.6*(max(x(mins:s,2))+min(x(mins:s,2)))/2; 18 | end 19 | % Ramp kappa down. 20 | for n=1:Max 21 | kappa=interval-step*n; 22 | options=odeset('RelTol',1e-4,'AbsTol',1e-4); 23 | [t,x]=ode45('Programs_20e',[0 tmax],[a,b],options); 24 | s=size(x(:,1),1); 25 | a=0;b=max(x(:,2)); 26 | kappadown(n)=0.6*(max(x(mins:s,2))+min(x(mins:s,2)))/2; 27 | end 28 | hold on 29 | rr=step:step:interval; 30 | plot(kappaup,rr,'b','LineWidth',10) 31 | plot(kappadown,interval-rr,'r','LineWidth',3) 32 | hold off 33 | fsize=15; 34 | axis([0 2 0 2]) 35 | xlabel('\langle \eta \rangle','FontSize',fsize) 36 | ylabel('\kappa','FontSize',fsize) 37 | set(gca,'XTick',0:1:2,'FontSize',fsize) 38 | set(gca,'YTick',0:1:2,'FontSize',fsize) 39 | 40 | % End of Programs 20f. -------------------------------------------------------------------------------- /Lynch R2016a/Programs_15h.m: -------------------------------------------------------------------------------- 1 | % Programs 15h - Bifurcation diagram showing ramp up and ramp down. 2 | % Chapter 15 - Poincare Maps and Nonautonomous Systems in the Plane. 3 | % Copyright Springer 2015. Stephen Lynch. 4 | 5 | % This models a beam oscillating between two magnets. 6 | % Please see: E. Ott, Chaos in Dynamical Systems (2nd edition), 7 | % Cambridge University Press, 2002. 8 | 9 | % Make sure Programs_15ff is in your directory. 10 | % Figure 15.14 11 | clear 12 | figure 13 | global Gamma; 14 | Max=4500;step=0.0001;interval=Max*step;a=1;b=0; 15 | % Ramp the amplitude up. 16 | for n=1:Max 17 | Gamma=step*n; 18 | [t,x]=ode45('Programs_15ff',0:(2*pi/1.25):(4*pi/1.25),[a,b]); 19 | a=x(2,1); 20 | b=x(2,2); 21 | rup(n)=sqrt((x(2,1))^2+(x(2,2))^2); 22 | end 23 | % Ramp the amplitude down. 24 | for n=1:Max 25 | Gamma=interval-step*n; 26 | [t,x]=ode45('Programs_15ff',0:(2*pi/1.25):(4*pi/1.25),[a,b]); 27 | a=x(2,1); 28 | b=x(2,2); 29 | rdown(n)=sqrt((x(2,1))^2+(x(2,2))^2); 30 | end 31 | hold on 32 | rr=step:step:interval; 33 | plot(rr,rup,'.','MarkerSize',1) 34 | plot(interval-rr,rdown,'r.','MarkerSize',1) 35 | hold off 36 | fsize=15; 37 | axis([0 .45 0 2]) 38 | xlabel('\Gamma','FontSize',fsize) 39 | ylabel('r','FontSize',fsize) 40 | title('Hysteresis in the Duffing System','FontSize',fsize) 41 | 42 | % End of Programs 15h. -------------------------------------------------------------------------------- /Lynch R2016a/license.txt: -------------------------------------------------------------------------------- 1 | Copyright (c) 2016, Stephen Lynch 2 | All rights reserved. 3 | 4 | Redistribution and use in source and binary forms, with or without 5 | modification, are permitted provided that the following conditions are 6 | met: 7 | 8 | * Redistributions of source code must retain the above copyright 9 | notice, this list of conditions and the following disclaimer. 10 | * Redistributions in binary form must reproduce the above copyright 11 | notice, this list of conditions and the following disclaimer in 12 | the documentation and/or other materials provided with the distribution 13 | 14 | THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" 15 | AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 16 | IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 17 | ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE 18 | LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR 19 | CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF 20 | SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS 21 | INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN 22 | CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 23 | ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE 24 | POSSIBILITY OF SUCH DAMAGE. 25 | -------------------------------------------------------------------------------- /LICENSE.txt: -------------------------------------------------------------------------------- 1 | 2 | Copyright (c) 2011, Stephen Lynch 3 | Copyright (c) 2009, Stephen Lynch 4 | All rights reserved. 5 | 6 | Redistribution and use in source and binary forms, with or without 7 | modification, are permitted provided that the following conditions are 8 | met: 9 | 10 | * Redistributions of source code must retain the above copyright 11 | notice, this list of conditions and the following disclaimer. 12 | * Redistributions in binary form must reproduce the above copyright 13 | notice, this list of conditions and the following disclaimer in 14 | the documentation and/or other materials provided with the distribution 15 | 16 | THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" 17 | AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 18 | IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 19 | ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE 20 | LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR 21 | CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF 22 | SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS 23 | INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN 24 | CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 25 | ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE 26 | POSSIBILITY OF SUCH DAMAGE. 27 | -------------------------------------------------------------------------------- /Lynch R2016a/Programs_16e.m: -------------------------------------------------------------------------------- 1 | % Programs 16e - Small-amplitude limit cycle for Example 1(i). 2 | % Chapter 16 - Local and Global Bifurcations. 3 | % Copyright Springer 2015 4 | % Please see Example 1 on page 339. The degree of F(x) is three and 5 | % the degree of g(x) is two. 6 | % The unstable limit cycle is in blue. 7 | clear;figure; 8 | hold on; 9 | plot(0,0,'b.','MarkerSize',15) 10 | a1=0.01;a2=1;b2=1;a3=1/3;xmin=-0.4;xmax=0.4;ymin=-0.4;ymax=0.5; 11 | options=odeset('RelTol',1e-8,'AbsTol',1e-8); 12 | % A trajectory inside the limit cycle. 13 | sys = @(t,x) [x(2)-a1*x(1)-a2*x(1)^2-a3*x(1)^3;-x(1)-a1*x(2)-b2*x(1)^2]; 14 | [t,xs] = ode45(sys,[0 50],[0.24 0],options); 15 | plot(xs(:,1),xs(:,2),'r'); 16 | % The approximate unstable limit cycle. 17 | sys = @(t,x) [x(2)-a1*x(1)-a2*x(1)^2-a3*x(1)^3;-x(1)-a1*x(2)-b2*x(1)^2]; 18 | [t,xs] = ode45(sys,[0 50],[0.2465 0],options); 19 | plot(xs(:,1),xs(:,2),'b','LineWidth',2); 20 | % A trajectory outside the limit cycle. 21 | sys = @(t,x) [x(2)-a1*x(1)-a2*x(1)^2-a3*x(1)^3;-x(1)-a1*x(2)-b2*x(1)^2]; 22 | [t,xs] = ode45(sys,[0 50],[0.25 0],options); 23 | plot(xs(:,1),xs(:,2),'r'); 24 | axis([xmin xmax ymin ymax]) 25 | fsize=15; 26 | set(gca,'XTick',xmin:0.2:xmax,'FontSize',fsize) 27 | set(gca,'YTick',ymin:0.2:ymax,'FontSize',fsize) 28 | xlabel('x(t)','FontSize',fsize) 29 | ylabel('y(t)','FontSize',fsize) 30 | title('One small-amplitude limit cycle (in blue) of a Lienard System') 31 | hold off; 32 | % End of Programs 16e. -------------------------------------------------------------------------------- /Lynch R2016a/Programs_15b.m: -------------------------------------------------------------------------------- 1 | % Programs 15b - Phase portraits for Hamiltonian systems with two degrees of freedom. 2 | % Chapter 15 - Poincare Maps and Nonautonomous Systems in the Plane. 3 | % Copyright Springer 2014. Stephen Lynch. 4 | 5 | % Poincare surfaces of section (Fig. 15.5(e)-(f)). 6 | % Quasiperiodic behavior. 7 | % The Hamiltonian equations. 8 | % Here p1=p(1),p2=p(2),q1=p(3),q2=p(4). 9 | 10 | deq=@(t,p) [-sqrt(2)*p(3);-p(4);sqrt(2)*p(1);p(2)]; 11 | options=odeset('RelTol',1e-4,'AbsTol',1e-4); 12 | [~,pp]=ode45(deq,[0 200],[.5,1.5,.5,0],options); 13 | 14 | % A 3-dimensional projection (Fig. 15.5(e)). 15 | subplot(2,1,1) 16 | fsize=15; 17 | plot3(pp(:,1),pp(:,2),pp(:,4)) 18 | 19 | deq=@(t,p) [-sqrt(2)*p(3);-p(4);sqrt(2)*p(1);p(2)]; 20 | options=odeset('RelTol',1e-4,'AbsTol',1e-4); 21 | [t,pq]=ode45(deq,[0 600],[.5,1.5,.5,0],options); 22 | 23 | 24 | % A 2-dimensional projection (Fig. 15.5(f)). 25 | % Determine where trajectory crosses q2=0 plane. 26 | k=0;p1_0=zeros(1,10^6);q1_0=zeros(1,10^6); 27 | for i=1:size(pq) 28 | if abs(pq(i,4))<0.1 29 | k=k+1; 30 | p1_0(k)=pq(i,1); 31 | q1_0(k)=pq(i,3); 32 | end 33 | end 34 | 35 | subplot(2,1,2) 36 | hold on 37 | axis([-1 1 -1 1]) 38 | set(gca,'XTick',-1:.5:1,'FontSize',fsize) 39 | set(gca,'YTick',-1:.5:1,'FontSize',fsize) 40 | xlabel('p_1','FontSize',fsize) 41 | ylabel('q_1','FontSize',fsize) 42 | plot(p1_0(1:k),q1_0(1:k),'+','MarkerSize',3) 43 | hold off 44 | 45 | % End of Programs 15b. -------------------------------------------------------------------------------- /Lynch R2016a/Program_7a.m: -------------------------------------------------------------------------------- 1 | % Program 7a - Signal corrupted with noise and power spectrum. 2 | % Chapter 7 - Image Processing. 3 | % Copyright Springer 2014. Stephen Lynch. 4 | 5 | Fs = 1000; % Sampling frequency. 6 | T = 1/Fs; % Sample time. 7 | L = 1000; % Length of signal. 8 | t = (0:L-1)*T; % Time vector. 9 | Amplitude1=0.7;Amplitude2=1;Frequency1=50;Frequency2=120; 10 | % Sum of a 50 Hz sinusoid and a 120 Hz sinusoid. 11 | x = Amplitude1*sin(2*pi*Frequency1*t) + Amplitude2*sin(2*pi*Frequency2*t); 12 | y = x + 2*randn(size(t)); % Sinusoids plus noise. 13 | subplot(2,1,1) 14 | plot(Fs*t(1:50),y(1:50)) 15 | fsize=15; 16 | axis([0 50 -6 8]); 17 | set(gca,'xtick',0:10:50,'FontSize',fsize) 18 | set(gca,'ytick',-6:2:8,'FontSize',fsize) 19 | xlabel('time ms','FontSize',fsize) 20 | ylabel('y','FontSize',fsize) 21 | 22 | 23 | NFFT = 2^nextpow2(L); % Next higher power of 2 from length of y. 24 | Y = fft(y,NFFT)/L; 25 | f = Fs/2*linspace(0,1,NFFT/2+1); % Linearly spaced vectors. 26 | subplot(2,1,2) % Plot single-sided amplitude spectrum. 27 | plot(f,2*abs(Y(1:NFFT/2+1))) 28 | fsize=15; 29 | axis([0 500 0 1]); 30 | set(gca,'xtick',0:100:500,'FontSize',fsize) 31 | set(gca,'ytick',0:0.5:1,'FontSize',fsize) 32 | xlabel('Frequency (Hz)','FontSize',fsize) 33 | ylabel('|Y(f)|','FontSize',fsize) 34 | 35 | % You can read off the amplitudes and frequencies from the fft. 36 | 37 | % End of Program_7a. -------------------------------------------------------------------------------- /Lynch R2016a/Programs_18a.m: -------------------------------------------------------------------------------- 1 | % Programs 18a - The Generalized Delta Learning Rule (Figure 18.7). 2 | % Chapter 18 - Neural Networks. 3 | % Copyright Springer 2014. Stephen Lynch. 4 | 5 | function Programs_18a 6 | % Load Boston housing data. 7 | load housing.txt 8 | X = housing(:,[6 9 13]); 9 | t = housing(:,14); 10 | 11 | % Scale to zero mean, unit variance and introduce bias on input. 12 | xmean = mean(X); 13 | xstd = std(X); 14 | X = (X-ones(size(X,1),1)*xmean)./(ones(size(X,1),1)*xstd); 15 | X = [ones(size(X,1),1) X]; 16 | tmean = (max(t)+min(t))/2; 17 | tstd = (max(t)-min(t))/2; 18 | t = (t-tmean)/tstd; 19 | 20 | % Initialise random weight vector. 21 | rng('default'); 22 | rng(123456) 23 | w(:,1) = 0.1*randn(size(X,2),1); 24 | y1 = tanh(X*w(:,1)); 25 | e1 = t-y1; 26 | mse(1) = var(e1); 27 | 28 | 29 | % Do numEpochs iterations. 30 | numEpochs = 50; 31 | numPatterns = size(X,1); 32 | eta = 0.001; 33 | k = 1; 34 | for m=1:numEpochs 35 | for n=1:numPatterns 36 | % Calculate feedforward output, error, and gradient. 37 | yk = tanh(X(n,:)*w(:,k)); 38 | err = yk-t(n); 39 | g = X(n,:)'*((1-yk^2)*err); 40 | % Update the weight. 41 | w(:,k+1) = w(:,k) - eta*g; 42 | k = k+1; 43 | end 44 | end 45 | figure; 46 | for m=1:size(w,1) 47 | plot(1:k,w(m,:)) 48 | hold on 49 | end 50 | 51 | fsize=15; 52 | set(gca,'XTick',0:5000:25000,'FontSize',fsize) 53 | set(gca,'YTick',-0.3:0.1:0.3,'FontSize',fsize) 54 | xlabel('Number of Iterations','FontSize',fsize) 55 | ylabel('Weights','FontSize',fsize) 56 | hold off 57 | 58 | % End of Programs 18a. 59 | -------------------------------------------------------------------------------- /Lynch R2016a/Programs_11d.m: -------------------------------------------------------------------------------- 1 | % Programs 11d - Two limit cycles in an economic Kaldor model. 2 | % Chapter 11 - Limit Cycles. 3 | % Copyright Springer 2014. Stephen Lynch. 4 | 5 | % J. Grasman and J.J. Wentzel, Co-existence of a limit cycle and an 6 | % equilibrium in Kaldor's business cycle model and its consequences, 7 | % J. Economic Behavior and Organization 24, 369-377 (1994). 8 | % NOTE: There is an error in the equations in the paper - corrected below. 9 | 10 | clear;figure; 11 | hold on 12 | % Plot the isoclines. 13 | ezplot('25*2^(-1/(0.015*x+0.00001)^2)+0.05*x+5*(320/y)^3-0.282*x',[10 100 200 500]) 14 | ezplot('25*2^(-1/(0.015*x+0.00001)^2)+0.05*x+5*(320/y)^3-0.05*y',[10 100 200 500]) 15 | alpha = 3; delta = 0.05; s = 0.282; 16 | 17 | % The Kaldor business cycle model. 18 | sys = @(t,x)[alpha*(25*2^(-1/(0.015*x(1)+0.00001)^2)+0.05*x(1)+5*(320/x(2))^3-s*x(1)); 25*2^(-1/(0.015*x(1)+0.00001)^2)+0.05*x(1)+5*(320/x(2))^3-delta*x(2)]; 19 | 20 | % Plot the stable limit cycle. 21 | [~,xs] = ode23s(sys,[0 100],[25 300]); 22 | plot(xs(:,1),xs(:,2),'r') 23 | % Plot the unstable limit cycle. 24 | [t,xb] = ode23s(sys,[0 -100],[60 355]); 25 | plot(xb(:,1),xb(:,2),'b') 26 | hold off 27 | 28 | axis([0 100 200 500]) 29 | fsize=15; 30 | set(gca,'XTick',0:20:100,'FontSize',fsize) 31 | set(gca,'YTick',200:50:400,'FontSize',fsize) 32 | title('Two limit cycles in a Kaldor economic model','FontSize',fsize) 33 | xlabel('y','FontSize',fsize) 34 | ylabel('k','FontSize',fsize) 35 | hold off 36 | 37 | % End of Programs 11d. -------------------------------------------------------------------------------- /Lynch R2016a/Program_5c.m: -------------------------------------------------------------------------------- 1 | % Chapter 5 - Electromagnetic Waves and Optical Resonators. 2 | % Program_5c - Bifurcation Diagram for a Nonlinear Optical Resonator. 3 | % Copyright Birkhauser 2014. Stephen Lynch. 4 | 5 | % Bifurcation diagram for a simple fiber resonator (Figures 5.13 & 5.16(a)). 6 | clear 7 | halfN=9999;N=2*halfN+1;N1=1+halfN; 8 | format long;E1=zeros(1,N);E2=zeros(1,N); 9 | Esqr=zeros(1,N);Esqr1=zeros(1,N);ptsup=zeros(1,N); 10 | C=0.345913; 11 | E1(1)=0;kappa=0.0225;Pmax=60;phi=0; 12 | 13 | % Ramp the power up 14 | for n=1:halfN 15 | E2(n+1)=E1(n)*exp(1i*(C*abs(E1(n))^2-phi)); 16 | E1(n+1)=1i*sqrt(1-kappa)*sqrt(n*Pmax/N1)+sqrt(kappa)*E2(n+1); 17 | Esqr(n+1)=abs(E1(n+1))^2; 18 | end 19 | 20 | % Ramp the power down 21 | for n=N1:N 22 | E2(n+1)=E1(n)*exp(1i*(C*abs(E1(n))^2-phi)); 23 | E1(n+1)=1i*sqrt(1-kappa)*sqrt(2*Pmax-n*Pmax/N1)+sqrt(kappa)*E2(n+1); 24 | Esqr(n+1)=abs(E1(n+1))^2; 25 | end 26 | 27 | for n=1:halfN 28 | Esqr1(n)=Esqr(N+1-n); 29 | ptsup(n)=n*Pmax/N1; 30 | end 31 | 32 | % Plot the bifurcation diagrams 33 | fsize=15; 34 | subplot(2,1,1) 35 | plot(Esqr(1:N),'.','MarkerSize',1) 36 | xlabel('Number of Ring Passes','FontSize',fsize); 37 | ylabel('Output','FontSize',fsize); 38 | 39 | subplot(2,1,2) 40 | hold on 41 | plot(ptsup(1:halfN),Esqr(1:halfN),'.','MarkerSize',1); 42 | plot(ptsup(1:halfN),Esqr1(1:halfN),'.','MarkerSize',1); 43 | xlabel('Input Power','FontSize',fsize); 44 | ylabel('Output Power','FontSize',fsize); 45 | hold off 46 | 47 | % End of Program_5c. 48 | -------------------------------------------------------------------------------- /Lynch R2016a/Programs_16a.m: -------------------------------------------------------------------------------- 1 | % Programs 16a - Determining the coefficients of the Lyapunov function 2 | % Chapter 16 - Local and Global Bifurcations. 3 | % for a Lienard system. 4 | % Copyright Birkhauser 2013. Stephen Lynch. 5 | 6 | % V3=[V30;V21;V12;V03], V4=[V40;V31;V22;V13;V04;eta4], 7 | % V5=[V50;V41;V32;V23;V14;V05],V6=[V60;V51;V42;V33;V24;V15;V06;eta6] 8 | % Symbolic Math toolbox required. 9 | 10 | % When determining coefficients of V_{4m} set V_{2m,2m}=0. 11 | % When determining coefficients of V_{4m+2} set V_{2m,2m+2}+V_{2m+2,2m}=0. 12 | 13 | clear all 14 | 15 | syms a1 a2 b2 a3 b3 a4 b4 a5 b5; 16 | A=[3 0 -2 0;0 0 1 0;0 -1 0 0;0 2 0 -3]; 17 | B=[b2; 0; a2; 0]; 18 | 19 | V3=A\B 20 | 21 | A=[0 -1 0 0 0 -1;0 3 0 -3 0 -2;0 0 0 1 0 -1;4 0 -2 0 0 0;0 0 2 0 -4 0; 0 0 1 0 0 0]; 22 | B=[a3; -2*a2*b2; 0; b3-2*a2^2;0;0]; 23 | 24 | V4=A\B 25 | 26 | A=[5 0 -2 0 0 0;0 0 3 0 -4 0;0 0 0 0 1 0;0 -1 0 0 0 0;0 4 0 -3 0 0;0 0 0 2 0 -5]; 27 | B=[b4-10*a2^2*b2/3;0;0;a4-2*a2^3;-2*a2*b3;0]; 28 | 29 | V5=A\B 30 | 31 | A=[6 0 -2 0 0 0 0 0;0 0 4 0 -4 0 0 0;0 0 0 0 2 0 -6 0;0 0 1 0 1 0 0 0; 32 | 0 -1 0 0 0 0 0 -1;0 5 0 -3 0 0 0 -3;0 0 0 3 0 -5 0 -3;0 0 0 0 0 1 0 -1]; 33 | B=[b5-6*a2*a4-4*a2^2*b2^2/3+8*a2^4;16*a2^4/3+4*a2^2*b3/3-8*a2*a4/3;0;0; 34 | a5-8*a2^3*b2/3;-2*a2*b4+8*a2^3*b2+2*a2*b2*b3-4*a4*b2; 35 | 16*a2^3*b2/3+4*a2*b2*b3/3-8*a4*b2/3;0]; 36 | 37 | V6=A\B 38 | 39 | L0=-a1 40 | eta4=V4(6,1); 41 | [n,d]=numden(-3/8*a3+1/4*a2*b2); 42 | L1=n 43 | a3=2*a2*b2; 44 | eta6=V6(8,1); 45 | [n,d]=numden(-5/16*a5+1/8*a2*b4-5/24*a2*b2*b3+5/12*a4*b2); 46 | L2=n 47 | 48 | % End of Programs 16a. -------------------------------------------------------------------------------- /Lynch R2016a/Program_5d.m: -------------------------------------------------------------------------------- 1 | % Program_5d - Animated Bifurcation Diagram for a Nonlinear Optical Resonator. 2 | % Chapter 5 - Electromagnetic Waves and Optical Resonators. 3 | % Copyright Springer 2014. Stephen Lynch. 4 | 5 | % Animated bifurcation diagram for a simple fiber ring resonator. 6 | clear 7 | halfN=7999;N=2*halfN+1;N1=1+halfN; 8 | E1=zeros(1,N);E2=zeros(1,N); 9 | Esqr=zeros(1,N);Esqr1=zeros(1,N);ptsup=zeros(1,N); 10 | for j = 1:60 11 | F(j) = getframe; 12 | format long; 13 | C=0.345913; 14 | % kappa increases from 0.001 to 0.06. 15 | E1(1)=0;kappa=0.001*j;Pmax=60;phi=0; 16 | 17 | % Ramp the power up 18 | for n=1:halfN 19 | E2(n+1)=E1(n)*exp(1i*(C*abs(E1(n))^2-phi)); 20 | E1(n+1)=1i*sqrt(1-kappa)*sqrt(n*Pmax/N1)+sqrt(kappa)*E2(n+1); 21 | Esqr(n+1)=abs(E1(n+1))^2; 22 | end 23 | 24 | % Ramp the power down 25 | for n=N1:N 26 | E2(n+1)=E1(n)*exp(1i*(C*abs(E1(n))^2-phi)); 27 | E1(n+1)=1i*sqrt(1-kappa)*sqrt(2*Pmax-n*Pmax/N1)+sqrt(kappa)*E2(n+1); 28 | Esqr(n+1)=abs(E1(n+1))^2; 29 | end 30 | 31 | for n=1:halfN 32 | Esqr1(n)=Esqr(N+1-n); 33 | ptsup(n)=n*Pmax/N1; 34 | end 35 | 36 | % Plot the bifurcation diagrams 37 | fsize=15; 38 | 39 | hold 40 | plot(ptsup(1:halfN),Esqr(1:halfN),'.','MarkerSize',1); 41 | plot(ptsup(1:halfN),Esqr1(1:halfN),'.','MarkerSize',1); 42 | xlabel('Input Power','FontSize',fsize); 43 | ylabel('Output Power','FontSize',fsize); 44 | axis([0 60 0 70]) 45 | title('Bifurcation Diagram for an Optical Resonator','FontSize',fsize); 46 | 47 | F(j) = getframe; 48 | 49 | end 50 | 51 | movie(F,5); 52 | 53 | % End of Program_5d. 54 | 55 | -------------------------------------------------------------------------------- /Lynch R2016a/Program_4c.m: -------------------------------------------------------------------------------- 1 | % Program_4c - The Mandelbrot Set in Color. 2 | % Chapter 4 - Complex Iterative Maps. 3 | % Program supplied by Steve Lord from The MathWorks. 4 | % Copyright Springer 2014. 5 | 6 | % Define parameters 7 | Nmax = 50; scale = 0.002; 8 | xmin = -2.4; xmax = 1.2; 9 | ymin = -1.5; ymax = 1.5; 10 | 11 | % Generate X and Y coordinates and Z complex values 12 | [x,y]=meshgrid(xmin:scale:xmax, ymin:scale:ymax); 13 | z = x+1i*y; 14 | 15 | % Generate w accumulation matrix and k counting matrix 16 | w = zeros(size(z)); 17 | k = zeros(size(z)); 18 | 19 | % Start off with the first step ... 20 | N = 0; 21 | 22 | % While N is less than Nmax and any k's are left as 0 23 | while N4 at this iteration and no 29 | % previous iteration get assigned the value of N 30 | k(~k & abs(w)>4) = N; 31 | end 32 | 33 | % If any k's are equal to 0 (i.e. the corresponding w's never blew up) set 34 | % them to the final iteration number 35 | k(k==0) = Nmax; 36 | 37 | % Open a new figure 38 | figure 39 | 40 | % Display the matrix as a surface 41 | s=pcolor(x,y,k); 42 | colormap jet(256); 43 | set(s,'edgecolor','none') 44 | 45 | % Adjust axis limits, ticks, and tick labels 46 | axis([xmin xmax -ymax ymax]) 47 | fontsize=15; 48 | set(gca,'XTick',xmin:0.4:xmax,'FontSize',fontsize) 49 | set(gca,'YTick',-ymax:0.5:ymax,'FontSize',fontsize) 50 | xlabel('Re z','FontSize',fontsize) 51 | ylabel('Im z','FontSize',fontsize) 52 | 53 | % End of Program_4c. -------------------------------------------------------------------------------- /Lynch R2016a/Programs_20a.m: -------------------------------------------------------------------------------- 1 | % Programs 20a - Hodgkin-Huxley equations spike train. 2 | % Chapter 20 - Binary Oscillator Computing. 3 | % Copyright Springer 2014. Stephen Lynch. 4 | 5 | % Hodgkin Huxley Integtrator with Synaptic Coupling - no time delay. 6 | clear; 7 | figure 8 | I=6.3; 9 | Gna=120;Gk=36;Gl=0.3; 10 | Vna=50;Vk=-77;Vl=-54.402;C=1; 11 | 12 | y=zeros(1,4); 13 | 14 | HHdeq=@(t,y) [(I-Gna*y(2)^3*y(3)*(y(1)-Vna)-Gk*y(4)^4*(y(1)-Vk)-Gl*(y(1)-Vl))/C; 0.1*(y(1)+40)/(1-exp(-0.1*(y(1)+40)))*(1-y(2))-4*exp(-0.0556*(y(1)+65))*y(2); 0.07*exp(-0.05*(y(1)+65))*(1-y(3))-1/(1+exp(-0.1*(y(1)+35)))*y(3);0.01*(y(1)+55)/(1-exp(-0.1*(y(1)+55)))*(1-y(4))-0.125*exp(-0.0125*(y(1)+65))*y(4)]; 15 | 16 | [t,ya]=ode45(HHdeq,[0 100],[15,0.01,0.5,0.4]); 17 | 18 | figure(1) 19 | plot(t,ya(:,1)) 20 | axis([0 100 -80 40]) 21 | fsize=15; 22 | set(gca,'XTick',0:20:100,'FontSize',fsize) 23 | set(gca,'YTick',-80:20:40,'FontSize',fsize) 24 | xlabel('Time (ms)','FontSize',fsize) 25 | ylabel('Voltage (mV)','FontSize',fsize) 26 | figure(2) 27 | subplot(3,1,1) 28 | plot(t,ya(:,2),'k') 29 | set(gca,'XTick',0:20:100,'FontSize',fsize) 30 | set(gca,'YTick',0:1,'FontSize',fsize) 31 | xlabel('Time (ms)','FontSize',fsize) 32 | ylabel('m(V)','FontSize',fsize) 33 | subplot(3,1,2) 34 | plot(t,ya(:,3),'r') 35 | set(gca,'XTick',0:20:100,'FontSize',fsize) 36 | set(gca,'YTick',0:1,'FontSize',fsize) 37 | xlabel('Time (ms)','FontSize',fsize) 38 | ylabel('h(V)','FontSize',fsize) 39 | subplot(3,1,3) 40 | plot(t,ya(:,4),'g') 41 | set(gca,'XTick',0:20:100,'FontSize',fsize) 42 | set(gca,'YTick',0:1,'FontSize',fsize) 43 | xlabel('Time (ms)','FontSize',fsize) 44 | ylabel('n(V)','FontSize',fsize) 45 | 46 | % End of Programs 20a. 47 | -------------------------------------------------------------------------------- /Lynch R2016a/Programs_18b.m: -------------------------------------------------------------------------------- 1 | % Programs 18b - Generalized Delta Learing Rule and Backpropagation of 2 | % errors. 3 | % Chapter 18 - Neural Networks. 4 | % for a multilayer network (Figure 18.8). 5 | % Copyright Springer 2014. Stephen Lynch. 6 | 7 | function Programs_18b 8 | % Load full Boston housing data. 9 | load housing.txt 10 | X = housing(:,1:13); 11 | t = housing(:,14); 12 | 13 | % Scale to zero mean, unit variance and introduce bias on input. 14 | xmean = mean(X); 15 | xstd = std(X); 16 | X = (X-ones(size(X,1),1)*xmean)./(ones(size(X,1),1)*xstd); 17 | X = [ones(size(X,1),1) X]; 18 | tmean = mean(t); 19 | tstd = std(t); 20 | t = (t-tmean)/tstd; 21 | 22 | % Iterate over a number of hidden nodes 23 | maxHidden = 2; 24 | for numHidden=1:maxHidden 25 | 26 | % Initialise random weight vector. 27 | % Wh are hidden weights, wo are output weights. 28 | rng('default'); 29 | rng(123456); 30 | Wh = 0.1*randn(size(X,2),numHidden); 31 | wo = 0.1*randn(numHidden+1,1); 32 | 33 | % Do numEpochs iterations of batch error back propagation. 34 | numEpochs = 2000; 35 | numPatterns = size(X,1); 36 | % Set eta. 37 | eta = 0.05/numPatterns; 38 | for i=1:numEpochs 39 | % Calculate outputs, errors, and gradients. 40 | phi = [ones(size(X,1),1) tanh(X*Wh)]; 41 | y = phi*wo; 42 | err = y-t; 43 | go = phi'*err; 44 | Gh = X'*((1-phi(:,2:numHidden+1).^2).*(err*wo(2:numHidden+1)')); 45 | % Perform gradient descent. 46 | wo = wo - eta*go; 47 | Wh = Wh - eta*Gh; 48 | % Update performance statistics. 49 | mse(i) = var(err); 50 | end 51 | 52 | plot(1:numEpochs, mse, '-') 53 | hold on 54 | end 55 | 56 | fsize=15; 57 | set(gca,'XTick',0:500:2000,'FontSize',fsize) 58 | set(gca,'YTick',0:0.5:1,'FontSize',fsize) 59 | xlabel('Number of Epochs','FontSize',fsize) 60 | ylabel('Mean Squared Error','FontSize',fsize) 61 | hold off 62 | 63 | % End of Programs 18b. 64 | 65 | 66 | 67 | -------------------------------------------------------------------------------- /Lynch R2016a/Programs_16f.m: -------------------------------------------------------------------------------- 1 | % Programs 16f - Small-amplitude limit cycles for Example 1(ii). 2 | % Chapter 16 - Local and Global Bifurcations. 3 | % Copyright Springer 2015 4 | % Please see Example 1 on page 339. The degree of F(x) is three and 5 | % the degree of g(x) is three. 6 | % The limit cycles are shown in blue. Please see Programs 16e. 7 | clear;figure; 8 | hold on; 9 | plot(0,0,'b.','MarkerSize',15) 10 | a1=0.01;a2=1;b2=1;a3=1/3;b3=2;xmin=-1;xmax=1;ymin=-0.6;ymax=1.3; 11 | options=odeset('RelTol',1e-8,'AbsTol',1e-8); 12 | sys = @(t,x) [x(2)-a1*x(1)-a2*x(1)^2-a3*x(1)^3;-x(1)-a1*x(2)-b2*x(1)^2-b3*x(1)^3]; 13 | [t,xs] = ode45(sys,[0 100],[0.28 0],options); 14 | plot(xs(:,1),xs(:,2),'r'); 15 | sys = @(t,x) [x(2)-a1*x(1)-a2*x(1)^2-a3*x(1)^3;-x(1)-a1*x(2)-b2*x(1)^2-b3*x(1)^3]; 16 | [t,xs] = ode45(sys,[0 100],[0.295 0],options); 17 | plot(xs(:,1),xs(:,2),'b','LineWidth',4); 18 | sys = @(t,x) [x(2)-a1*x(1)-a2*x(1)^2-a3*x(1)^3;-x(1)-a1*x(2)-b2*x(1)^2-b3*x(1)^3]; 19 | [t,xs] = ode45(sys,[0 100],[0.3 0],options); 20 | plot(xs(:,1),xs(:,2),'r'); 21 | sys = @(t,x) [x(2)-a1*x(1)-a2*x(1)^2-a3*x(1)^3;-x(1)-a1*x(2)-b2*x(1)^2-b3*x(1)^3]; 22 | [t,xs] = ode45(sys,[0 100],[0.48 0],options); 23 | plot(xs(:,1),xs(:,2),'r'); 24 | sys = @(t,x) [x(2)-a1*x(1)-a2*x(1)^2-a3*x(1)^3;-x(1)-a1*x(2)-b2*x(1)^2-b3*x(1)^3]; 25 | [t,xs] = ode45(sys,[0 50],[0.519 0],options); 26 | plot(xs(:,1),xs(:,2),'b','LineWidth',4); 27 | sys = @(t,x) [x(2)-a1*x(1)-a2*x(1)^2-a3*x(1)^3;-x(1)-a1*x(2)-b2*x(1)^2-b3*x(1)^3]; 28 | [t,xs] = ode45(sys,[0 50],[0.54 0],options); 29 | plot(xs(:,1),xs(:,2),'r'); 30 | axis([xmin xmax ymin ymax]) 31 | fsize=15; 32 | set(gca,'XTick',xmin:0.2:xmax,'FontSize',fsize) 33 | set(gca,'YTick',ymin:0.2:ymax,'FontSize',fsize) 34 | xlabel('x(t)','FontSize',fsize) 35 | ylabel('y(t)','FontSize',fsize) 36 | title('Two small-amplitude limit cycles (in blue) of a Lienard system') 37 | hold off; 38 | % End of Programs 16f. -------------------------------------------------------------------------------- /Lynch R2016a/Programs_18e.m: -------------------------------------------------------------------------------- 1 | % Programs 18e - Bifurcation Diagram for a Simple Bistable Neuromodule. 2 | % Chapter 18 - Neural Networks. 3 | % Copyright Springer 2014. Stephen Lynch. 4 | 5 | % Bifurcation diagram for a two-neuron module. (See Figure 18.15). 6 | % Vary bias b1. 7 | clear all 8 | format long; 9 | halfN=1000;N=2*halfN+1;N1=1+halfN;Max=10;a=1;alpha=0.3; 10 | x=zeros(1,N);y=zeros(1,N); 11 | b2=3;w11=7;w12=-4;w21=5;start=-5; 12 | x(1)=-10;y(1)=-3; 13 | 14 | % Ramp the power up 15 | for n=1:halfN 16 | b1=(start+n*Max/halfN); 17 | x(n+1)=b1+w11*(exp(a*x(n))-exp(-a*x(n)))/(exp(a*x(n))+exp(-a*x(n)))+w12*(exp(alpha*y(n))-exp(-alpha*y(n)))/(exp(alpha*y(n))+exp(-alpha*y(n))); 18 | y(n+1)=b2+w21*(exp(a*x(n))-exp(-a*x(n)))/(exp(a*x(n))+exp(-a*x(n))); 19 | end 20 | 21 | % Ramp the power down 22 | for n=N1:N 23 | b1=(start+2*Max-n*Max/halfN); 24 | x(n+1)=b1+w11*(exp(a*x(n))-exp(-a*x(n)))/(exp(a*x(n))+exp(-a*x(n)))+w12*(exp(alpha*y(n))-exp(-alpha*y(n)))/(exp(alpha*y(n))+exp(-alpha*y(n))); 25 | y(n+1)=b2+w21*(exp(a*x(n))-exp(-a*x(n)))/(exp(a*x(n))+exp(-a*x(n))); 26 | end 27 | 28 | % Plot the bifurcation diagrams 29 | fsize=14; 30 | subplot(2,1,1) 31 | hold on 32 | set(gca,'XTick',0:halfN/2:N,'FontSize',fsize); 33 | set(gca,'YTick',-Max:5:Max,'FontSize',fsize); 34 | plot(x(1:N),'-','MarkerSize',1,'color','k') 35 | xlabel('Number of Iterations','FontSize',fsize); 36 | ylabel('x_n','FontSize',fsize); 37 | hold off 38 | x1=zeros(1,N);w=zeros(1,N); 39 | 40 | for n=1:halfN 41 | x1(n)=x(N+1-n); 42 | w(n)=start+n*Max/halfN; 43 | end 44 | 45 | subplot(2,1,2) 46 | hold on 47 | set(gca,'XTick',start:5:start+Max,'FontSize',fsize); 48 | set(gca,'YTick',-Max:5:Max,'FontSize',fsize); 49 | plot(w(1:halfN),x(1:halfN),'-','MarkerSize',1,'color','k'); 50 | plot(w(1:halfN),x1(1:halfN),'-','MarkerSize',1,'color','r'); 51 | xlabel('b_1','FontSize',fsize); 52 | ylabel('x_n','FontSize',fsize); 53 | hold off 54 | 55 | % End of Programs 18e. 56 | 57 | 58 | 59 | -------------------------------------------------------------------------------- /Lynch R2016a/Program_1b.m: -------------------------------------------------------------------------------- 1 | % Program 1b - Plots and differential equations. 2 | % Chapter 1 - A Tutorial Introduction to MATLAB and the Symbolic Math Package. 3 | % Copyright Birkhaser 2014. Stephen Lynch. 4 | 5 | % These commands should be run in the Command Window. 6 | % Copy the commands into the Command Window. 7 | 8 | clear 9 | % Plot a simple function. 10 | x=-2:.01:2; 11 | plot(x,x.^2) 12 | 13 | % Plot two functions on one graph. 14 | t=0:.1:100; 15 | y1=exp(-.1*t).*cos(t);y2=cos(t); 16 | plot(t,y1,t,y2),legend('y1','y2') 17 | 18 | % Symbolic plots. 19 | ezplot('x^2',[-2,2]) 20 | ezplot('exp(-t)*sin(t)'),xlabel('time'),ylabel('current'),title('decay') 21 | 22 | % 3-D plots on a 50x50 grid. 23 | ezcontour('y^2/2-x^2/2+x^4/4',[-2,2],50) 24 | ezsurf('y^2/2-x^2/2+x^4/4',[-2,2],50) 25 | ezsurfc('y^2/2-x^2/2+x^4/4',[-2,2],50) 26 | 27 | % Parametric plot. 28 | ezplot('t^3-4*t','t^2',[-3,3]) 29 | 30 | % 3-D parametric plot. 31 | ezplot3('sin(t)','cos(t)','t',[-10,10]) 32 | 33 | % Symbolic solutions to ODEs. 34 | dsolve('Dx=-x/t') 35 | dsolve('D2x+5*Dx+6*x=10*sin(t)','x(0)=0','Dx(0)=0') 36 | 37 | % Linear systems of ODEs. 38 | [x,y]=dsolve('Dx=3*x+4*y','Dy=-4*x+3*y') 39 | [x,y]=dsolve('Dx=x^2','Dy=y^2','x(0)=1,y(0)=1') 40 | 41 | % A 3-D linear system. 42 | [x,y,z]=dsolve('Dx=x','Dy=y','Dz=-z') 43 | 44 | % Numerical solutionms to ODEs. 45 | deq1=@(t,x) x(1)*(.1-.01*x(1)); 46 | [t,xa]=ode45(deq1,[0 100],50); 47 | plot(t,xa(:,1)) 48 | 49 | % A 2-D system. 50 | deq2=@(t,x) [.1*x(1)+x(2);-x(1)+.1*x(2)]; 51 | [t,xb]=ode45(deq2,[0 50],[.01,0]); 52 | plot(xb(:,1),xb(:,2)) 53 | 54 | % A 3-D system. 55 | deq3=@(t,x) [x(3)-x(1);-x(2);x(3)-17*x(1)+16]; 56 | [t,xc]=ode45(deq3,[0 20],[.8,.8,.8]); 57 | plot3(xc(:,1),xc(:,2),xc(:,3)) 58 | 59 | % A stiff system. 60 | deq4=@(t,x) [x(2);1000*(1-(x(1))^2)*x(2)-x(1)]; 61 | [t,xd]=ode23s(deq4,[0 3000],[.01,0]); 62 | plot(xd(:,1),xd(:,2)) 63 | 64 | % x versus t. 65 | plot(t,xd(:,1)) 66 | 67 | % End of Program 1b. 68 | 69 | 70 | 71 | 72 | 73 | 74 | -------------------------------------------------------------------------------- /Lynch R2016a/Program_1a.m: -------------------------------------------------------------------------------- 1 | % Program 1a: Tutorial One: The Basics. 2 | % Chapter 1 - A Tutorial Introduction to MATLAB and the Symbolic Math Package. 3 | % Copyright Birkhaser 2014. Stephen Lynch. 4 | 5 | % These commands should be run in the Command Window. If you are new to MATLAB 6 | % copy the commands and hit ENTER at the end of each line. 7 | % You can cut and paste the following commands into the Command Window. 8 | 9 | clear % Remove items from workspace. 10 | 3^2*4-3*2^5*(4-2) % Simple arithmetic. 11 | sqrt(16) % Square root. 12 | u=1:2:9 % A vector. 13 | v=u.^2 % Square the elements. 14 | A=[1,2;3,4] % A 2x2 matrix. 15 | A' % The transpose. 16 | det(A) % The determinant. 17 | B=[0,3,1;.3,0,0;0,.5,0] % A 3x3 matrix. 18 | eig(B) % The eigenvalues of B. 19 | [Vects,Vals]=eig(B) % Eigenvectors and eigenvalues. 20 | C=[100;200;300] % A 3x1 matrix. 21 | D=B*C % Matrix multiplication. 22 | E=B^4 % Powers of matrices. 23 | z1=1+i % Complex numbers. 24 | z2=1-i 25 | z3=2+i 26 | z4=2*z1-z2*z3 % Complex arithmetic. 27 | abs(z1) % Modulus. 28 | real(z1) % Real part. 29 | imag(z1) % Imaginary part. 30 | exp(i*z1) % Exponential. 31 | sym(1/2)+sym(3/4) % Symbolic arithmetic. 32 | 1/2+3/4 % Double precision. 33 | vpa(pi,50) % Variable precision. 34 | syms x y z % Symbolic objects 35 | z=x^3-y^3 36 | factor(z) % Factorization. 37 | expand(6*cos(t-pi/4)) % Expansion. 38 | simplify(z/(x-y)) % Simplification. 39 | syms x y 40 | [x,y]=solve(x^2-x==0,2*x*y-y^2==0) % Solving simultaneous equations. 41 | syms x mu 42 | f=mu*x*(1-x) % Define a function. 43 | subs(f,x,1/2) % Evaluate f(1/2). 44 | fof=subs(f,x,f) % Composite function. 45 | limit(x/sin(x),x,0) % Limits. 46 | diff(f,x) % Differentiation. 47 | syms x y 48 | diff(x^2+3*x*y-2*y^2,y,2) % Partial differentiation. 49 | int(sin(x)*cos(x),x,0,pi/2) % Integration. 50 | int(1/x,x,0,inf) % Improper integration. 51 | syms n s w 52 | s1=symsum(1/n^2,1,inf) % Symbolic summation. 53 | g=exp(x) 54 | taylor(g,'Order',10) % Taylor series up to order 10. 55 | syms a w 56 | laplace(x^3) % Laplace transform. 57 | ilaplace(1/(s-a)) % Inverse transform. 58 | fourier(exp(-x^2)) % Fourier transform. 59 | ifourier(pi/(1+w^2)) % Inverse transform. 60 | 61 | % End of Program 1a. 62 | -------------------------------------------------------------------------------- /Lynch R2016a/Programs_18c.m: -------------------------------------------------------------------------------- 1 | % Programs 18c - The Hopfield Network Used as an Associative Memory. 2 | % Chapter 18 - Neural Networks. 3 | % Copyright Birkhauser 2013. Stephen Lynch. 4 | 5 | function Programs_18c 6 | clear all 7 | % The 81-dimensional fundamental memories (Figure 17.12). 8 | X = [-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 -1 -1 -1 -1 -1 1 1 -1 1 1 -1 -1 -1 -1 1 1 -1 1 1 -1 -1 -1 -1 1 1 -1 1 1 -1 -1 -1 -1 1 1 -1 1 1 -1 -1 -1 -1 1 1 -1 1 1 -1 -1 -1 -1 -1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1; 9 | -1 -1 -1 1 1 1 -1 -1 -1 -1 -1 -1 1 1 1 -1 -1 -1 -1 -1 -1 1 1 1 -1 -1 -1 -1 -1 -1 1 1 1 -1 -1 -1 -1 -1 -1 1 1 1 -1 -1 -1 -1 -1 -1 1 1 1 -1 -1 -1 -1 -1 -1 1 1 1 -1 -1 -1 -1 -1 -1 1 1 1 -1 -1 -1 -1 -1 -1 1 1 1 -1 -1 -1; 10 | -1 -1 1 1 1 1 1 -1 -1 -1 1 -1 -1 -1 -1 -1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 -1 -1 -1 -1 -1 -1 -1 1 -1 -1 -1 -1 -1 -1 -1 1 -1 -1 -1 -1 -1 -1 -1 1 -1 -1 -1 -1 -1 -1 -1 1 -1 -1 -1 -1 -1 -1 -1 1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 -1; 11 | -1 1 1 -1 -1 -1 1 1 -1 -1 1 1 -1 -1 -1 1 1 -1 -1 1 1 -1 -1 -1 1 1 -1 -1 1 1 -1 -1 -1 1 1 -1 -1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 1 1 -1 -1 -1 -1 -1 -1 -1 1 1 -1 -1 -1 -1 -1 -1 -1 1 1 -1 -1 -1 -1 -1 -1 -1 1 1 -1; 12 | 1 1 1 1 1 1 -1 -1 -1 1 1 -1 -1 -1 -1 -1 -1 -1 1 1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 -1 -1 -1 1 1 -1 -1 1 1 -1 -1 -1 1 1 -1 -1 1 1 -1 -1 -1 1 1 -1 -1 1 1 -1 -1 -1 1 1 -1 -1 1 1 -1 -1 -1 1 1 1 1 1 1 -1 -1 -1]; 13 | 14 | % Load data. 15 | X = X([1 2 3 4 5],:); 16 | numPatterns = size(X,1); 17 | numInputs = size(X,2); 18 | % Plot the fundamental memories. They will appear in Figure 1. 19 | figure 20 | plotHopfieldData(X) 21 | 22 | % STEP 1. Calculate the weight matrix using Hebb's postulate. 23 | W = (X'*X - numPatterns*eye(numInputs))/numInputs; 24 | 25 | % STEP 2. Set a probe vector using a predefined noiselevel. The probe 26 | % vector is a distortion of one of the fundamental memories. 27 | noiseLevel = 1/3; 28 | patInd = ceil(numPatterns*rand(1,1)); 29 | xold = (2*(rand(numInputs,1)> noiseLevel)-1).*X(patInd,:)'; 30 | 31 | % STEP 3. Asynchronous updates of the elements of the probe vector until it 32 | % converges. To guarantee convergence, the algorithm performs at least 33 | % numPatterns=81 iterations even though convergence generally occurs before 34 | % this. 35 | figure 36 | converged = 0; 37 | x=xold; 38 | while converged==0, 39 | p=randperm(numInputs); 40 | for n=1:numInputs 41 | r = x(p(n)); 42 | x(p(n)) = hsign(W(p(n),:)*x, r); 43 | plotHopfieldVector(x); 44 | pause(0.01); 45 | end 46 | % STEP 4. Check for convergence. 47 | if (all(x==xold)) 48 | break; 49 | end 50 | xold = x; 51 | end 52 | 53 | % Step 3. Update the elements asynchronously. 54 | function y = hsign(a, r) 55 | y(a>0) = 1; 56 | y(a==0) = r; 57 | y(a<0) = -1; 58 | 59 | % Plot the fundamental memories. 60 | function plotHopfieldData(X) 61 | numPatterns = size(X,1); 62 | numRows = ceil(sqrt(numPatterns)); 63 | numCols = ceil(numPatterns/numRows); 64 | for i=1:numPatterns 65 | subplot(numRows, numCols, i); 66 | axis equal; 67 | plotHopfieldVector(X(i,:)) 68 | end 69 | 70 | % Plot the sequence of iterations for the probe vector. The sequence is 71 | % shown in Figure 2. Note that 81 iterations. You can exit by pressing 72 | % Ctrl-Shift-C, if you wish to interupt the program. 73 | function plotHopfieldVector(x) 74 | cla; 75 | numInputs = length(x); 76 | numRows = ceil(sqrt(numInputs)); 77 | numCols = ceil(numInputs/numRows); 78 | for m=1:numRows 79 | for n=1:numCols 80 | xind = numRows*(m-1)+n; 81 | if xind > numInputs 82 | break; 83 | elseif x(xind)==1 84 | rectangle('Position', [n-1 numRows-m 1 1], 'FaceColor', 'k'); 85 | elseif x(xind)==-1 86 | rectangle('Position', [n-1 numRows-m 1 1], 'FaceColor', 'w'); 87 | end 88 | end 89 | end 90 | set(gca, 'XLim', [0 numCols], 'XTick', []); 91 | set(gca, 'YLim', [0 numRows], 'YTick', []); 92 | 93 | % End of Programs 18c. -------------------------------------------------------------------------------- /Lynch R2016a/Programs_14d.m: -------------------------------------------------------------------------------- 1 | % Programs 14d - Lyapunov exponents of the Lorenz system. 2 | % Chapter 14 - Three-Dimensional Autonomous Systems and Chaos. 3 | % Copyright Springer 2014. Stephen Lynch. 4 | 5 | % Special thanks to Vasiliy Govorukhin for allowing me to use his M-files. 6 | % For continuous and discrete systems see the Lyapunov Exponents Toolbox of 7 | % Steve Siu at the mathworks/matlabcentral/fileexchange. 8 | 9 | % Reference. 10 | % A. Wolf, J. B. Swift, H. L. Swinney, and J. A. Vastano, "Determining Lyapunov Exponents from a Time Series," Physica D, 11 | % Vol. 16, pp. 285-317, 1985. 12 | % You must read the above paper to understand how the program works. 13 | 14 | % Lyapunov exponents for the Lorenz system below are: 15 | % L_1 = 0.9022, L_2 = 0.0003, L_3 = -14.5691 when tend=10,000. 16 | 17 | function [Texp,Lexp]=lyapunov(n,rhs_ext_fcn,fcn_integrator,tstart,stept,tend,ystart,ioutp); 18 | 19 | n=3;rhs_ext_fcn=@lorenz_ext;fcn_integrator=@ode45; 20 | tstart=0;stept=0.5;tend=300; 21 | ystart=[1 1 1];ioutp=10; 22 | n1=n; n2=n1*(n1+1); 23 | 24 | % Number of steps. 25 | nit = round((tend-tstart)/stept); 26 | 27 | % Memory allocation. 28 | y=zeros(n2,1); cum=zeros(n1,1); y0=y; 29 | gsc=cum; znorm=cum; 30 | 31 | % Initial values. 32 | y(1:n)=ystart(:); 33 | 34 | for i=1:n1 y((n1+1)*i)=1.0; end; 35 | 36 | t=tstart; 37 | 38 | % Main loop. 39 | for ITERLYAP=1:nit 40 | % Solutuion of extended ODE system. 41 | [T,Y] = feval(fcn_integrator,rhs_ext_fcn,[t t+stept],y); 42 | t=t+stept; 43 | y=Y(size(Y,1),:); 44 | 45 | for i=1:n1 46 | for j=1:n1 y0(n1*i+j)=y(n1*j+i); end; 47 | end; 48 | 49 | % Construct new orthonormal basis by Gram-Schmidt. 50 | 51 | znorm(1)=0.0; 52 | for j=1:n1 znorm(1)=znorm(1)+y0(n1*j+1)^2; end; 53 | 54 | znorm(1)=sqrt(znorm(1)); 55 | 56 | for j=1:n1 y0(n1*j+1)=y0(n1*j+1)/znorm(1); end; 57 | 58 | for j=2:n1 59 | for k=1:(j-1) 60 | gsc(k)=0.0; 61 | for l=1:n1 gsc(k)=gsc(k)+y0(n1*l+j)*y0(n1*l+k); end; 62 | end; 63 | 64 | for k=1:n1 65 | for l=1:(j-1) 66 | y0(n1*k+j)=y0(n1*k+j)-gsc(l)*y0(n1*k+l); 67 | end; 68 | end; 69 | 70 | znorm(j)=0.0; 71 | for k=1:n1 znorm(j)=znorm(j)+y0(n1*k+j)^2; end; 72 | znorm(j)=sqrt(znorm(j)); 73 | 74 | for k=1:n1 y0(n1*k+j)=y0(n1*k+j)/znorm(j); end; 75 | end; 76 | 77 | % Update running vector magnitudes. 78 | 79 | for k=1:n1 cum(k)=cum(k)+log(znorm(k)); end; 80 | 81 | % Normalize exponent. 82 | 83 | for k=1:n1 84 | lp(k)=cum(k)/(t-tstart); 85 | end; 86 | 87 | % Output modification. 88 | 89 | if ITERLYAP==1 90 | Lexp=lp; 91 | Texp=t; 92 | else 93 | Lexp=[Lexp; lp]; 94 | Texp=[Texp; t]; 95 | end; 96 | 97 | for i=1:n1 98 | for j=1:n1 99 | y(n1*j+i)=y0(n1*i+j); 100 | end; 101 | end; 102 | 103 | end; 104 | 105 | % Show the Lyapunov exponent values on the graph. 106 | str1=num2str(Lexp(nit,1));str2=num2str(Lexp(nit,2));str3=num2str(Lexp(nit,3)); 107 | plot(Texp,Lexp); 108 | title('Dynamics of Lyapunov Exponents'); 109 | text(235,1.5,'\lambda_1=','Fontsize',10); 110 | text(250,1.5,str1); 111 | text(235,-1,'\lambda_2=','Fontsize',10); 112 | text(250,-1,str2); 113 | text(235,-13.8,'\lambda_3=','Fontsize',10); 114 | text(250,-13.8,str3); 115 | xlabel('Time'); ylabel('Lyapunov Exponents'); 116 | % End of plot 117 | 118 | function f=lorenz_ext(t,X); 119 | % 120 | % Values of parameters. 121 | SIGMA = 10; R = 28; BETA = 8/3; 122 | 123 | x=X(1); y=X(2); z=X(3); 124 | 125 | Y= [X(4), X(7), X(10); 126 | X(5), X(8), X(11); 127 | X(6), X(9), X(12)]; 128 | 129 | f=zeros(9,1); 130 | 131 | %Lorenz equation. 132 | f(1)=SIGMA*(y-x); 133 | f(2)=-x*z+R*x-y; 134 | f(3)=x*y-BETA*z; 135 | 136 | %Linearized system. 137 | Jac=[-SIGMA, SIGMA, 0; 138 | R-z, -1, -x; 139 | y, x, -BETA]; 140 | 141 | %Variational equation. 142 | f(4:12)=Jac*Y; 143 | 144 | %Output data must be a column vector. 145 | 146 | % End of Programs 14d. 147 | 148 | 149 | -------------------------------------------------------------------------------- /Index of MATLAB Files.txt: -------------------------------------------------------------------------------- 1 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 2 | % DYNAMICAL SYSTEMS WITH APPLICATIONS USING MATLAB 2nd Edition % 3 | % COPYRIGHT SPRINGER/BIRKHAUSER 2014 STEPHEN LYNCH % 4 | % MATLAB FILES UPDATED FOR R2016a % 5 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 6 | 7 | Text and JPEG Files 8 | 9 | Book Table of Contents.txt --- Contents of the book. 10 | housing.txt --- Data file to be used in Chapter 18. 11 | Index of MATLAB Files.txt --- This file! 12 | lena.jpg --- An image file used in Chapter 7. 13 | 14 | Pdf Files 15 | MMU_Mock_Exam_1.pdf 16 | MMU_Mock_Exam_2.pdf 17 | 18 | MATLAB and MuPAD Files 19 | 20 | Program_1a.m --- Tutorial One (You should run it in the Command Window) 21 | Program_1b.m --- Tutorial Two (You should run it in the Command Window) 22 | Program_2a.m --- Solving Recurrence Relations 23 | Program_2b.m --- The Leslie Matrix 24 | Program_3a.m --- Graphical Iteration of the Tent Map 25 | Program_3b.m --- Graphical Iteration of the Logistic Map 26 | Program_3c.m --- Computing a Lyapunov Exponent for the Logistic Map 27 | Program_3d.m --- Bifurcation Diagram of the Logistic Map 28 | Program_3e.m --- Bifurcation Diagram of the Gaussian Map 29 | Program_3f.m --- Chaotic Attractor for the Henon Map 30 | Program_3g.m --- Computation of the Lyapunov Exponents of the Henon Map 31 | Program_4a.m --- A Julia Set 32 | Program_4b.m --- The Mandelbrot Set 33 | Program_4c.m --- Color Mandelbrot Set 34 | Program_5a.m --- Determining Fixed Points of Period One 35 | Program_5b.m --- Chaotic Attractor of the Ikeda Map 36 | Program_5c.m --- Bifurcation Diagram of the Simple Fiber Ring Resonator 37 | Program_5d.m --- Animation of a Bifurcation Diagram 38 | Program_6a.m --- The Koch Curve 39 | Program_6b.m --- The Sierpinski Triangle 40 | Program_6c.m --- Barnsley's Fern 41 | Program_6d.m --- Multifractal tau Curve 42 | Program_6e.m --- Multifractal D_q Curve 43 | Program_6f.m --- Multifractal f-alpha Curve 44 | Program_7a.m --- Signal Corrupted with Noise and Power Spectrum 45 | Program_7b.m --- Chaotic Attractor and Power Spectrum 46 | Program_7c.m --- Fast Fourier Transform, Low Pass on Lena.jpg 47 | Program_8a.m --- Simple ODE Exercises 48 | Program_8b.m --- Population Model 49 | Program_8c.m --- Chemical Kinetics 50 | Program_8d.mn --- MuPAD Commands for Series Solution 51 | Program_8e.m --- Series and Numerical Solution van der Pol 52 | vectorfield.m --- Program to Plot Vector Field of a Planar System 53 | Program_9a.m --- Phase Portrait of a Linear System 54 | Program_9b.m --- Phase Portrait of a Nonlinear System 55 | Programs_10a.m --- Competing Species Model 56 | Programs_10b.m --- Predator-Prey Model 57 | Programs_11a.m --- Limit Cycle of a Van der Pol System 58 | Programs_11b.m --- Non-Convex Limit Cycle of a Lienard System 59 | Programs_11c.m --- Limit Cycle of Fitzhugh-Nagumo Model of Neuron 60 | 61 | Programs_11d.m -—- Two limit cycles in an economic Kaldor model 62 | Programs_11e.m --- Perturbation methods for Example 7 63 | Programs_11f.mn --- Perturbation methods for Example 7 using MuPAD 64 | Programs_12a.m --- The Double Well Potential 65 | Programs_12b.m --- Lyapunov Function for a Hopfield Network 66 | Programs_13a.m --- Animation of a Simple Curve 67 | Programs_13b.m --- Finding Critical Points 68 | Programs_13c.m --- Needed for Programs_13d 69 | Programs_13d.m --- Hopf Bifurcation Animation 70 | Programs_14a.m --- The Lorenz Attractor 71 | Programs_14b.m --- Chua's Double Scroll Attractor 72 | Programs_14c.m --- The Chapman Cycle (Ozone Production) 73 | Programs_14d.m --- Computing the Lyapunov Exponents of the Lorenz System 74 | Programs_14e.m --- Time Series for a Stiff Belousov-Zhabotinski Reaction 75 | Programs_14f.m --- Animation of Chua circuit bifurcation 76 | Programs_15a.m --- Simple Poincare Map 77 | Programs_15b.m --- Poincare Surface of Section for Hamiltonians 78 | Programs_15c.m --- Phase Portrait for the Nonautonomous Duffing System 79 | Programs_15d.m --- Poincare Section of the Duffing System 80 | Programs_15e.m --- Hamiltonian with two Degrees of Freedom 81 | Programs_15f.m --- Needed for Programs_15g 82 | Programs_15g.m --- Bifurcation Diagram of a Periodically Forced Ribbon between magnets 83 | Programs_15ff.m --- Needed for Programs_15g 84 | Programs_15h.m --- Bifurcation Diagram of a Periodically Forced Ribbon between magnets 85 | Programs_15fff.m --- Needed for Programs_15k 86 | Programs_15k.m --- Bifurcation Diagram of a Periodically Forced Pendulum 87 | Programs_16a.m --- Computing Focal Values 88 | Programs_16b.mn --- MuPAD Commands for Groebner Bases 89 | Programs_16c.m --- Needed for Programs_16d 90 | Programs_16d.m --- Animation of a Homoclinic Bifurcation 91 | 92 | Programs_16e.m --- One small-amplitude limit cycle in a Lienard system 93 | 94 | Programs_16f.m --- One small-amplitude limit cycle in a Lienard system 95 | Programs_18a.m --- Generalized Delta Rule (Boston Housing Data) 96 | Programs_18b.m --- Backpropagation of Errors 97 | Programs_18c.m --- Discrete Hopfield Network 98 | Programs_18d.m --- Chaotic Attractor of a Simple Neuromodule 99 | Programs_18e.m --- Bifurcation Diagram of a Simple Neuromodule 100 | Programs_19a.m --- Chaos Control in the Logistic Map 101 | Programs_19b.m --- Chaos Control in the Henon Map 102 | Programs_19c.m --- Synchronization Between Two Lorenz Systems 103 | Programs_20a.m --- Hodgkin-Huxley Spike Train 104 | Programs_20b.m --- Needed for Programs_20d 105 | Programs_20c.m --- Needed for Prohrams_20d 106 | Programs_20d.m --- Time Series of Binary Oscillator Half Adder 107 | Programs_20e.m --- Needed for Programs_20f 108 | Programs_20f.m --- Bifurcation Diagram of a Josephson Junction 109 | Programs_20g.m --- Pinched Hysteresis of a HP Labs Memristor 110 | Prohrams_20h.m --- Animation of a Josephson junction threshold oscillator 111 | 112 | Simulink Files 113 | 114 | Simulink_1.slx --- Series Resistor-Inductor Circuit 115 | Simulink_2.slx --- Series Resistor-Inductor-Capacitor Circuit 116 | Simulink_3.slx --- The van der Pol Circuit 117 | Simulink_4.slx --- A Periodically Forced Pendulum 118 | Simulink_5.slx --- Simple Fiber Ring (SFR) Resonator 119 | Simulink_6.slx --- Chaos Control in a SFR Resonator 120 | Simulink_7.slx --- The Lorenz Equations 121 | Simulink_8.slx --- Lorenz Equations and Chaos Synchronization 122 | Simulink_9.slx --- SFR Gaussian Input 123 | Simulink_10.slx --- Generalized Synchronization -------------------------------------------------------------------------------- /Lynch R2016a/Index of MATLAB Files.txt: -------------------------------------------------------------------------------- 1 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 2 | % DYNAMICAL SYSTEMS WITH APPLICATIONS USING MATLAB 2nd Edition % 3 | % COPYRIGHT SPRINGER/BIRKHAUSER 2014 STEPHEN LYNCH % 4 | % MATLAB FILES UPDATED FOR R2016a % 5 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 6 | 7 | Text and JPEG Files 8 | 9 | Book Table of Contents.txt --- Contents of the book. 10 | housing.txt --- Data file to be used in Chapter 18. 11 | Index of MATLAB Files.txt --- This file! 12 | lena.jpg --- An image file used in Chapter 7. 13 | 14 | Pdf Files 15 | MMU_Mock_Exam_1.pdf 16 | MMU_Mock_Exam_2.pdf 17 | 18 | MATLAB and MuPAD Files 19 | 20 | Program_1a.m --- Tutorial One (You should run it in the Command Window) 21 | Program_1b.m --- Tutorial Two (You should run it in the Command Window) 22 | Program_2a.m --- Solving Recurrence Relations 23 | Program_2b.m --- The Leslie Matrix 24 | Program_3a.m --- Graphical Iteration of the Tent Map 25 | Program_3b.m --- Graphical Iteration of the Logistic Map 26 | Program_3c.m --- Computing a Lyapunov Exponent for the Logistic Map 27 | Program_3d.m --- Bifurcation Diagram of the Logistic Map 28 | Program_3e.m --- Bifurcation Diagram of the Gaussian Map 29 | Program_3f.m --- Chaotic Attractor for the Henon Map 30 | Program_3g.m --- Computation of the Lyapunov Exponents of the Henon Map 31 | Program_4a.m --- A Julia Set 32 | Program_4b.m --- The Mandelbrot Set 33 | Program_4c.m --- Color Mandelbrot Set 34 | Program_5a.m --- Determining Fixed Points of Period One 35 | Program_5b.m --- Chaotic Attractor of the Ikeda Map 36 | Program_5c.m --- Bifurcation Diagram of the Simple Fiber Ring Resonator 37 | Program_5d.m --- Animation of a Bifurcation Diagram 38 | Program_6a.m --- The Koch Curve 39 | Program_6b.m --- The Sierpinski Triangle 40 | Program_6c.m --- Barnsley's Fern 41 | Program_6d.m --- Multifractal tau Curve 42 | Program_6e.m --- Multifractal D_q Curve 43 | Program_6f.m --- Multifractal f-alpha Curve 44 | Program_7a.m --- Signal Corrupted with Noise and Power Spectrum 45 | Program_7b.m --- Chaotic Attractor and Power Spectrum 46 | Program_7c.m --- Fast Fourier Transform, Low Pass on Lena.jpg 47 | Program_8a.m --- Simple ODE Exercises 48 | Program_8b.m --- Population Model 49 | Program_8c.m --- Chemical Kinetics 50 | Program_8d.mn --- MuPAD Commands for Series Solution 51 | Program_8e.m --- Series and Numerical Solution van der Pol 52 | vectorfield.m --- Program to Plot Vector Field of a Planar System 53 | Program_9a.m --- Phase Portrait of a Linear System 54 | Program_9b.m --- Phase Portrait of a Nonlinear System 55 | Programs_10a.m --- Competing Species Model 56 | Programs_10b.m --- Predator-Prey Model 57 | Programs_11a.m --- Limit Cycle of a Van der Pol System 58 | Programs_11b.m --- Non-Convex Limit Cycle of a Lienard System 59 | Programs_11c.m --- Limit Cycle of Fitzhugh-Nagumo Model of Neuron 60 | 61 | Programs_11d.m -—- Two limit cycles in an economic Kaldor model 62 | Programs_11e.m --- Perturbation methods for Example 7 63 | Programs_11f.mn --- Perturbation methods for Example 7 using MuPAD 64 | Programs_12a.m --- The Double Well Potential 65 | Programs_12b.m --- Lyapunov Function for a Hopfield Network 66 | Programs_13a.m --- Animation of a Simple Curve 67 | Programs_13b.m --- Finding Critical Points 68 | Programs_13c.m --- Needed for Programs_13d 69 | Programs_13d.m --- Hopf Bifurcation Animation 70 | Programs_14a.m --- The Lorenz Attractor 71 | Programs_14b.m --- Chua's Double Scroll Attractor 72 | Programs_14c.m --- The Chapman Cycle (Ozone Production) 73 | Programs_14d.m --- Computing the Lyapunov Exponents of the Lorenz System 74 | Programs_14e.m --- Time Series for a Stiff Belousov-Zhabotinski Reaction 75 | Programs_14f.m --- Animation of Chua circuit bifurcation 76 | Programs_15a.m --- Simple Poincare Map 77 | Programs_15b.m --- Poincare Surface of Section for Hamiltonians 78 | Programs_15c.m --- Phase Portrait for the Nonautonomous Duffing System 79 | Programs_15d.m --- Poincare Section of the Duffing System 80 | Programs_15e.m --- Hamiltonian with two Degrees of Freedom 81 | Programs_15f.m --- Needed for Programs_15g 82 | Programs_15g.m --- Bifurcation Diagram of a Periodically Forced Ribbon between magnets 83 | Programs_15ff.m --- Needed for Programs_15g 84 | Programs_15h.m --- Bifurcation Diagram of a Periodically Forced Ribbon between magnets 85 | Programs_15fff.m --- Needed for Programs_15k 86 | Programs_15k.m --- Bifurcation Diagram of a Periodically Forced Pendulum 87 | Programs_16a.m --- Computing Focal Values 88 | Programs_16b.mn --- MuPAD Commands for Groebner Bases 89 | Programs_16c.m --- Needed for Programs_16d 90 | Programs_16d.m --- Animation of a Homoclinic Bifurcation 91 | 92 | Programs_16e.m --- One small-amplitude limit cycle in a Lienard system 93 | 94 | Programs_16f.m --- One small-amplitude limit cycle in a Lienard system 95 | Programs_18a.m --- Generalized Delta Rule (Boston Housing Data) 96 | Programs_18b.m --- Backpropagation of Errors 97 | Programs_18c.m --- Discrete Hopfield Network 98 | Programs_18d.m --- Chaotic Attractor of a Simple Neuromodule 99 | Programs_18e.m --- Bifurcation Diagram of a Simple Neuromodule 100 | Programs_19a.m --- Chaos Control in the Logistic Map 101 | Programs_19b.m --- Chaos Control in the Henon Map 102 | Programs_19c.m --- Synchronization Between Two Lorenz Systems 103 | Programs_20a.m --- Hodgkin-Huxley Spike Train 104 | Programs_20b.m --- Needed for Programs_20d 105 | Programs_20c.m --- Needed for Prohrams_20d 106 | Programs_20d.m --- Time Series of Binary Oscillator Half Adder 107 | Programs_20e.m --- Needed for Programs_20f 108 | Programs_20f.m --- Bifurcation Diagram of a Josephson Junction 109 | Programs_20g.m --- Pinched Hysteresis of a HP Labs Memristor 110 | Prohrams_20h.m --- Animation of a Josephson junction threshold oscillator 111 | 112 | Simulink Files 113 | 114 | Simulink_1.slx --- Series Resistor-Inductor Circuit 115 | Simulink_2.slx --- Series Resistor-Inductor-Capacitor Circuit 116 | Simulink_3.slx --- The van der Pol Circuit 117 | Simulink_4.slx --- A Periodically Forced Pendulum 118 | Simulink_5.slx --- Simple Fiber Ring (SFR) Resonator 119 | Simulink_6.slx --- Chaos Control in a SFR Resonator 120 | Simulink_7.slx --- The Lorenz Equations 121 | Simulink_8.slx --- Lorenz Equations and Chaos Synchronization 122 | Simulink_9.slx --- SFR Gaussian Input 123 | Simulink_10.slx --- Generalized Synchronization -------------------------------------------------------------------------------- /Lynch R2016a/housing.txt: -------------------------------------------------------------------------------- 1 | 0.00632 18.00 2.310 0 0.5380 6.5750 65.20 4.0900 1 296.0 15.30 396.90 4.98 24.00 2 | 0.02731 0.00 7.070 0 0.4690 6.4210 78.90 4.9671 2 242.0 17.80 396.90 9.14 21.60 3 | 0.02729 0.00 7.070 0 0.4690 7.1850 61.10 4.9671 2 242.0 17.80 392.83 4.03 34.70 4 | 0.03237 0.00 2.180 0 0.4580 6.9980 45.80 6.0622 3 222.0 18.70 394.63 2.94 33.40 5 | 0.06905 0.00 2.180 0 0.4580 7.1470 54.20 6.0622 3 222.0 18.70 396.90 5.33 36.20 6 | 0.02985 0.00 2.180 0 0.4580 6.4300 58.70 6.0622 3 222.0 18.70 394.12 5.21 28.70 7 | 0.08829 12.50 7.870 0 0.5240 6.0120 66.60 5.5605 5 311.0 15.20 395.60 12.43 22.90 8 | 0.14455 12.50 7.870 0 0.5240 6.1720 96.10 5.9505 5 311.0 15.20 396.90 19.15 27.10 9 | 0.21124 12.50 7.870 0 0.5240 5.6310 100.00 6.0821 5 311.0 15.20 386.63 29.93 16.50 10 | 0.17004 12.50 7.870 0 0.5240 6.0040 85.90 6.5921 5 311.0 15.20 386.71 17.10 18.90 11 | 0.22489 12.50 7.870 0 0.5240 6.3770 94.30 6.3467 5 311.0 15.20 392.52 20.45 15.00 12 | 0.11747 12.50 7.870 0 0.5240 6.0090 82.90 6.2267 5 311.0 15.20 396.90 13.27 18.90 13 | 0.09378 12.50 7.870 0 0.5240 5.8890 39.00 5.4509 5 311.0 15.20 390.50 15.71 21.70 14 | 0.62976 0.00 8.140 0 0.5380 5.9490 61.80 4.7075 4 307.0 21.00 396.90 8.26 20.40 15 | 0.63796 0.00 8.140 0 0.5380 6.0960 84.50 4.4619 4 307.0 21.00 380.02 10.26 18.20 16 | 0.62739 0.00 8.140 0 0.5380 5.8340 56.50 4.4986 4 307.0 21.00 395.62 8.47 19.90 17 | 1.05393 0.00 8.140 0 0.5380 5.9350 29.30 4.4986 4 307.0 21.00 386.85 6.58 23.10 18 | 0.78420 0.00 8.140 0 0.5380 5.9900 81.70 4.2579 4 307.0 21.00 386.75 14.67 17.50 19 | 0.80271 0.00 8.140 0 0.5380 5.4560 36.60 3.7965 4 307.0 21.00 288.99 11.69 20.20 20 | 0.72580 0.00 8.140 0 0.5380 5.7270 69.50 3.7965 4 307.0 21.00 390.95 11.28 18.20 21 | 1.25179 0.00 8.140 0 0.5380 5.5700 98.10 3.7979 4 307.0 21.00 376.57 21.02 13.60 22 | 0.85204 0.00 8.140 0 0.5380 5.9650 89.20 4.0123 4 307.0 21.00 392.53 13.83 19.60 23 | 1.23247 0.00 8.140 0 0.5380 6.1420 91.70 3.9769 4 307.0 21.00 396.90 18.72 15.20 24 | 0.98843 0.00 8.140 0 0.5380 5.8130 100.00 4.0952 4 307.0 21.00 394.54 19.88 14.50 25 | 0.75026 0.00 8.140 0 0.5380 5.9240 94.10 4.3996 4 307.0 21.00 394.33 16.30 15.60 26 | 0.84054 0.00 8.140 0 0.5380 5.5990 85.70 4.4546 4 307.0 21.00 303.42 16.51 13.90 27 | 0.67191 0.00 8.140 0 0.5380 5.8130 90.30 4.6820 4 307.0 21.00 376.88 14.81 16.60 28 | 0.95577 0.00 8.140 0 0.5380 6.0470 88.80 4.4534 4 307.0 21.00 306.38 17.28 14.80 29 | 0.77299 0.00 8.140 0 0.5380 6.4950 94.40 4.4547 4 307.0 21.00 387.94 12.80 18.40 30 | 1.00245 0.00 8.140 0 0.5380 6.6740 87.30 4.2390 4 307.0 21.00 380.23 11.98 21.00 31 | 1.13081 0.00 8.140 0 0.5380 5.7130 94.10 4.2330 4 307.0 21.00 360.17 22.60 12.70 32 | 1.35472 0.00 8.140 0 0.5380 6.0720 100.00 4.1750 4 307.0 21.00 376.73 13.04 14.50 33 | 1.38799 0.00 8.140 0 0.5380 5.9500 82.00 3.9900 4 307.0 21.00 232.60 27.71 13.20 34 | 1.15172 0.00 8.140 0 0.5380 5.7010 95.00 3.7872 4 307.0 21.00 358.77 18.35 13.10 35 | 1.61282 0.00 8.140 0 0.5380 6.0960 96.90 3.7598 4 307.0 21.00 248.31 20.34 13.50 36 | 0.06417 0.00 5.960 0 0.4990 5.9330 68.20 3.3603 5 279.0 19.20 396.90 9.68 18.90 37 | 0.09744 0.00 5.960 0 0.4990 5.8410 61.40 3.3779 5 279.0 19.20 377.56 11.41 20.00 38 | 0.08014 0.00 5.960 0 0.4990 5.8500 41.50 3.9342 5 279.0 19.20 396.90 8.77 21.00 39 | 0.17505 0.00 5.960 0 0.4990 5.9660 30.20 3.8473 5 279.0 19.20 393.43 10.13 24.70 40 | 0.02763 75.00 2.950 0 0.4280 6.5950 21.80 5.4011 3 252.0 18.30 395.63 4.32 30.80 41 | 0.03359 75.00 2.950 0 0.4280 7.0240 15.80 5.4011 3 252.0 18.30 395.62 1.98 34.90 42 | 0.12744 0.00 6.910 0 0.4480 6.7700 2.90 5.7209 3 233.0 17.90 385.41 4.84 26.60 43 | 0.14150 0.00 6.910 0 0.4480 6.1690 6.60 5.7209 3 233.0 17.90 383.37 5.81 25.30 44 | 0.15936 0.00 6.910 0 0.4480 6.2110 6.50 5.7209 3 233.0 17.90 394.46 7.44 24.70 45 | 0.12269 0.00 6.910 0 0.4480 6.0690 40.00 5.7209 3 233.0 17.90 389.39 9.55 21.20 46 | 0.17142 0.00 6.910 0 0.4480 5.6820 33.80 5.1004 3 233.0 17.90 396.90 10.21 19.30 47 | 0.18836 0.00 6.910 0 0.4480 5.7860 33.30 5.1004 3 233.0 17.90 396.90 14.15 20.00 48 | 0.22927 0.00 6.910 0 0.4480 6.0300 85.50 5.6894 3 233.0 17.90 392.74 18.80 16.60 49 | 0.25387 0.00 6.910 0 0.4480 5.3990 95.30 5.8700 3 233.0 17.90 396.90 30.81 14.40 50 | 0.21977 0.00 6.910 0 0.4480 5.6020 62.00 6.0877 3 233.0 17.90 396.90 16.20 19.40 51 | 0.08873 21.00 5.640 0 0.4390 5.9630 45.70 6.8147 4 243.0 16.80 395.56 13.45 19.70 52 | 0.04337 21.00 5.640 0 0.4390 6.1150 63.00 6.8147 4 243.0 16.80 393.97 9.43 20.50 53 | 0.05360 21.00 5.640 0 0.4390 6.5110 21.10 6.8147 4 243.0 16.80 396.90 5.28 25.00 54 | 0.04981 21.00 5.640 0 0.4390 5.9980 21.40 6.8147 4 243.0 16.80 396.90 8.43 23.40 55 | 0.01360 75.00 4.000 0 0.4100 5.8880 47.60 7.3197 3 469.0 21.10 396.90 14.80 18.90 56 | 0.01311 90.00 1.220 0 0.4030 7.2490 21.90 8.6966 5 226.0 17.90 395.93 4.81 35.40 57 | 0.02055 85.00 0.740 0 0.4100 6.3830 35.70 9.1876 2 313.0 17.30 396.90 5.77 24.70 58 | 0.01432 100.00 1.320 0 0.4110 6.8160 40.50 8.3248 5 256.0 15.10 392.90 3.95 31.60 59 | 0.15445 25.00 5.130 0 0.4530 6.1450 29.20 7.8148 8 284.0 19.70 390.68 6.86 23.30 60 | 0.10328 25.00 5.130 0 0.4530 5.9270 47.20 6.9320 8 284.0 19.70 396.90 9.22 19.60 61 | 0.14932 25.00 5.130 0 0.4530 5.7410 66.20 7.2254 8 284.0 19.70 395.11 13.15 18.70 62 | 0.17171 25.00 5.130 0 0.4530 5.9660 93.40 6.8185 8 284.0 19.70 378.08 14.44 16.00 63 | 0.11027 25.00 5.130 0 0.4530 6.4560 67.80 7.2255 8 284.0 19.70 396.90 6.73 22.20 64 | 0.12650 25.00 5.130 0 0.4530 6.7620 43.40 7.9809 8 284.0 19.70 395.58 9.50 25.00 65 | 0.01951 17.50 1.380 0 0.4161 7.1040 59.50 9.2229 3 216.0 18.60 393.24 8.05 33.00 66 | 0.03584 80.00 3.370 0 0.3980 6.2900 17.80 6.6115 4 337.0 16.10 396.90 4.67 23.50 67 | 0.04379 80.00 3.370 0 0.3980 5.7870 31.10 6.6115 4 337.0 16.10 396.90 10.24 19.40 68 | 0.05789 12.50 6.070 0 0.4090 5.8780 21.40 6.4980 4 345.0 18.90 396.21 8.10 22.00 69 | 0.13554 12.50 6.070 0 0.4090 5.5940 36.80 6.4980 4 345.0 18.90 396.90 13.09 17.40 70 | 0.12816 12.50 6.070 0 0.4090 5.8850 33.00 6.4980 4 345.0 18.90 396.90 8.79 20.90 71 | 0.08826 0.00 10.810 0 0.4130 6.4170 6.60 5.2873 4 305.0 19.20 383.73 6.72 24.20 72 | 0.15876 0.00 10.810 0 0.4130 5.9610 17.50 5.2873 4 305.0 19.20 376.94 9.88 21.70 73 | 0.09164 0.00 10.810 0 0.4130 6.0650 7.80 5.2873 4 305.0 19.20 390.91 5.52 22.80 74 | 0.19539 0.00 10.810 0 0.4130 6.2450 6.20 5.2873 4 305.0 19.20 377.17 7.54 23.40 75 | 0.07896 0.00 12.830 0 0.4370 6.2730 6.00 4.2515 5 398.0 18.70 394.92 6.78 24.10 76 | 0.09512 0.00 12.830 0 0.4370 6.2860 45.00 4.5026 5 398.0 18.70 383.23 8.94 21.40 77 | 0.10153 0.00 12.830 0 0.4370 6.2790 74.50 4.0522 5 398.0 18.70 373.66 11.97 20.00 78 | 0.08707 0.00 12.830 0 0.4370 6.1400 45.80 4.0905 5 398.0 18.70 386.96 10.27 20.80 79 | 0.05646 0.00 12.830 0 0.4370 6.2320 53.70 5.0141 5 398.0 18.70 386.40 12.34 21.20 80 | 0.08387 0.00 12.830 0 0.4370 5.8740 36.60 4.5026 5 398.0 18.70 396.06 9.10 20.30 81 | 0.04113 25.00 4.860 0 0.4260 6.7270 33.50 5.4007 4 281.0 19.00 396.90 5.29 28.00 82 | 0.04462 25.00 4.860 0 0.4260 6.6190 70.40 5.4007 4 281.0 19.00 395.63 7.22 23.90 83 | 0.03659 25.00 4.860 0 0.4260 6.3020 32.20 5.4007 4 281.0 19.00 396.90 6.72 24.80 84 | 0.03551 25.00 4.860 0 0.4260 6.1670 46.70 5.4007 4 281.0 19.00 390.64 7.51 22.90 85 | 0.05059 0.00 4.490 0 0.4490 6.3890 48.00 4.7794 3 247.0 18.50 396.90 9.62 23.90 86 | 0.05735 0.00 4.490 0 0.4490 6.6300 56.10 4.4377 3 247.0 18.50 392.30 6.53 26.60 87 | 0.05188 0.00 4.490 0 0.4490 6.0150 45.10 4.4272 3 247.0 18.50 395.99 12.86 22.50 88 | 0.07151 0.00 4.490 0 0.4490 6.1210 56.80 3.7476 3 247.0 18.50 395.15 8.44 22.20 89 | 0.05660 0.00 3.410 0 0.4890 7.0070 86.30 3.4217 2 270.0 17.80 396.90 5.50 23.60 90 | 0.05302 0.00 3.410 0 0.4890 7.0790 63.10 3.4145 2 270.0 17.80 396.06 5.70 28.70 91 | 0.04684 0.00 3.410 0 0.4890 6.4170 66.10 3.0923 2 270.0 17.80 392.18 8.81 22.60 92 | 0.03932 0.00 3.410 0 0.4890 6.4050 73.90 3.0921 2 270.0 17.80 393.55 8.20 22.00 93 | 0.04203 28.00 15.040 0 0.4640 6.4420 53.60 3.6659 4 270.0 18.20 395.01 8.16 22.90 94 | 0.02875 28.00 15.040 0 0.4640 6.2110 28.90 3.6659 4 270.0 18.20 396.33 6.21 25.00 95 | 0.04294 28.00 15.040 0 0.4640 6.2490 77.30 3.6150 4 270.0 18.20 396.90 10.59 20.60 96 | 0.12204 0.00 2.890 0 0.4450 6.6250 57.80 3.4952 2 276.0 18.00 357.98 6.65 28.40 97 | 0.11504 0.00 2.890 0 0.4450 6.1630 69.60 3.4952 2 276.0 18.00 391.83 11.34 21.40 98 | 0.12083 0.00 2.890 0 0.4450 8.0690 76.00 3.4952 2 276.0 18.00 396.90 4.21 38.70 99 | 0.08187 0.00 2.890 0 0.4450 7.8200 36.90 3.4952 2 276.0 18.00 393.53 3.57 43.80 100 | 0.06860 0.00 2.890 0 0.4450 7.4160 62.50 3.4952 2 276.0 18.00 396.90 6.19 33.20 101 | 0.14866 0.00 8.560 0 0.5200 6.7270 79.90 2.7778 5 384.0 20.90 394.76 9.42 27.50 102 | 0.11432 0.00 8.560 0 0.5200 6.7810 71.30 2.8561 5 384.0 20.90 395.58 7.67 26.50 103 | 0.22876 0.00 8.560 0 0.5200 6.4050 85.40 2.7147 5 384.0 20.90 70.80 10.63 18.60 104 | 0.21161 0.00 8.560 0 0.5200 6.1370 87.40 2.7147 5 384.0 20.90 394.47 13.44 19.30 105 | 0.13960 0.00 8.560 0 0.5200 6.1670 90.00 2.4210 5 384.0 20.90 392.69 12.33 20.10 106 | 0.13262 0.00 8.560 0 0.5200 5.8510 96.70 2.1069 5 384.0 20.90 394.05 16.47 19.50 107 | 0.17120 0.00 8.560 0 0.5200 5.8360 91.90 2.2110 5 384.0 20.90 395.67 18.66 19.50 108 | 0.13117 0.00 8.560 0 0.5200 6.1270 85.20 2.1224 5 384.0 20.90 387.69 14.09 20.40 109 | 0.12802 0.00 8.560 0 0.5200 6.4740 97.10 2.4329 5 384.0 20.90 395.24 12.27 19.80 110 | 0.26363 0.00 8.560 0 0.5200 6.2290 91.20 2.5451 5 384.0 20.90 391.23 15.55 19.40 111 | 0.10793 0.00 8.560 0 0.5200 6.1950 54.40 2.7778 5 384.0 20.90 393.49 13.00 21.70 112 | 0.10084 0.00 10.010 0 0.5470 6.7150 81.60 2.6775 6 432.0 17.80 395.59 10.16 22.80 113 | 0.12329 0.00 10.010 0 0.5470 5.9130 92.90 2.3534 6 432.0 17.80 394.95 16.21 18.80 114 | 0.22212 0.00 10.010 0 0.5470 6.0920 95.40 2.5480 6 432.0 17.80 396.90 17.09 18.70 115 | 0.14231 0.00 10.010 0 0.5470 6.2540 84.20 2.2565 6 432.0 17.80 388.74 10.45 18.50 116 | 0.17134 0.00 10.010 0 0.5470 5.9280 88.20 2.4631 6 432.0 17.80 344.91 15.76 18.30 117 | 0.13158 0.00 10.010 0 0.5470 6.1760 72.50 2.7301 6 432.0 17.80 393.30 12.04 21.20 118 | 0.15098 0.00 10.010 0 0.5470 6.0210 82.60 2.7474 6 432.0 17.80 394.51 10.30 19.20 119 | 0.13058 0.00 10.010 0 0.5470 5.8720 73.10 2.4775 6 432.0 17.80 338.63 15.37 20.40 120 | 0.14476 0.00 10.010 0 0.5470 5.7310 65.20 2.7592 6 432.0 17.80 391.50 13.61 19.30 121 | 0.06899 0.00 25.650 0 0.5810 5.8700 69.70 2.2577 2 188.0 19.10 389.15 14.37 22.00 122 | 0.07165 0.00 25.650 0 0.5810 6.0040 84.10 2.1974 2 188.0 19.10 377.67 14.27 20.30 123 | 0.09299 0.00 25.650 0 0.5810 5.9610 92.90 2.0869 2 188.0 19.10 378.09 17.93 20.50 124 | 0.15038 0.00 25.650 0 0.5810 5.8560 97.00 1.9444 2 188.0 19.10 370.31 25.41 17.30 125 | 0.09849 0.00 25.650 0 0.5810 5.8790 95.80 2.0063 2 188.0 19.10 379.38 17.58 18.80 126 | 0.16902 0.00 25.650 0 0.5810 5.9860 88.40 1.9929 2 188.0 19.10 385.02 14.81 21.40 127 | 0.38735 0.00 25.650 0 0.5810 5.6130 95.60 1.7572 2 188.0 19.10 359.29 27.26 15.70 128 | 0.25915 0.00 21.890 0 0.6240 5.6930 96.00 1.7883 4 437.0 21.20 392.11 17.19 16.20 129 | 0.32543 0.00 21.890 0 0.6240 6.4310 98.80 1.8125 4 437.0 21.20 396.90 15.39 18.00 130 | 0.88125 0.00 21.890 0 0.6240 5.6370 94.70 1.9799 4 437.0 21.20 396.90 18.34 14.30 131 | 0.34006 0.00 21.890 0 0.6240 6.4580 98.90 2.1185 4 437.0 21.20 395.04 12.60 19.20 132 | 1.19294 0.00 21.890 0 0.6240 6.3260 97.70 2.2710 4 437.0 21.20 396.90 12.26 19.60 133 | 0.59005 0.00 21.890 0 0.6240 6.3720 97.90 2.3274 4 437.0 21.20 385.76 11.12 23.00 134 | 0.32982 0.00 21.890 0 0.6240 5.8220 95.40 2.4699 4 437.0 21.20 388.69 15.03 18.40 135 | 0.97617 0.00 21.890 0 0.6240 5.7570 98.40 2.3460 4 437.0 21.20 262.76 17.31 15.60 136 | 0.55778 0.00 21.890 0 0.6240 6.3350 98.20 2.1107 4 437.0 21.20 394.67 16.96 18.10 137 | 0.32264 0.00 21.890 0 0.6240 5.9420 93.50 1.9669 4 437.0 21.20 378.25 16.90 17.40 138 | 0.35233 0.00 21.890 0 0.6240 6.4540 98.40 1.8498 4 437.0 21.20 394.08 14.59 17.10 139 | 0.24980 0.00 21.890 0 0.6240 5.8570 98.20 1.6686 4 437.0 21.20 392.04 21.32 13.30 140 | 0.54452 0.00 21.890 0 0.6240 6.1510 97.90 1.6687 4 437.0 21.20 396.90 18.46 17.80 141 | 0.29090 0.00 21.890 0 0.6240 6.1740 93.60 1.6119 4 437.0 21.20 388.08 24.16 14.00 142 | 1.62864 0.00 21.890 0 0.6240 5.0190 100.00 1.4394 4 437.0 21.20 396.90 34.41 14.40 143 | 3.32105 0.00 19.580 1 0.8710 5.4030 100.00 1.3216 5 403.0 14.70 396.90 26.82 13.40 144 | 4.09740 0.00 19.580 0 0.8710 5.4680 100.00 1.4118 5 403.0 14.70 396.90 26.42 15.60 145 | 2.77974 0.00 19.580 0 0.8710 4.9030 97.80 1.3459 5 403.0 14.70 396.90 29.29 11.80 146 | 2.37934 0.00 19.580 0 0.8710 6.1300 100.00 1.4191 5 403.0 14.70 172.91 27.80 13.80 147 | 2.15505 0.00 19.580 0 0.8710 5.6280 100.00 1.5166 5 403.0 14.70 169.27 16.65 15.60 148 | 2.36862 0.00 19.580 0 0.8710 4.9260 95.70 1.4608 5 403.0 14.70 391.71 29.53 14.60 149 | 2.33099 0.00 19.580 0 0.8710 5.1860 93.80 1.5296 5 403.0 14.70 356.99 28.32 17.80 150 | 2.73397 0.00 19.580 0 0.8710 5.5970 94.90 1.5257 5 403.0 14.70 351.85 21.45 15.40 151 | 1.65660 0.00 19.580 0 0.8710 6.1220 97.30 1.6180 5 403.0 14.70 372.80 14.10 21.50 152 | 1.49632 0.00 19.580 0 0.8710 5.4040 100.00 1.5916 5 403.0 14.70 341.60 13.28 19.60 153 | 1.12658 0.00 19.580 1 0.8710 5.0120 88.00 1.6102 5 403.0 14.70 343.28 12.12 15.30 154 | 2.14918 0.00 19.580 0 0.8710 5.7090 98.50 1.6232 5 403.0 14.70 261.95 15.79 19.40 155 | 1.41385 0.00 19.580 1 0.8710 6.1290 96.00 1.7494 5 403.0 14.70 321.02 15.12 17.00 156 | 3.53501 0.00 19.580 1 0.8710 6.1520 82.60 1.7455 5 403.0 14.70 88.01 15.02 15.60 157 | 2.44668 0.00 19.580 0 0.8710 5.2720 94.00 1.7364 5 403.0 14.70 88.63 16.14 13.10 158 | 1.22358 0.00 19.580 0 0.6050 6.9430 97.40 1.8773 5 403.0 14.70 363.43 4.59 41.30 159 | 1.34284 0.00 19.580 0 0.6050 6.0660 100.00 1.7573 5 403.0 14.70 353.89 6.43 24.30 160 | 1.42502 0.00 19.580 0 0.8710 6.5100 100.00 1.7659 5 403.0 14.70 364.31 7.39 23.30 161 | 1.27346 0.00 19.580 1 0.6050 6.2500 92.60 1.7984 5 403.0 14.70 338.92 5.50 27.00 162 | 1.46336 0.00 19.580 0 0.6050 7.4890 90.80 1.9709 5 403.0 14.70 374.43 1.73 50.00 163 | 1.83377 0.00 19.580 1 0.6050 7.8020 98.20 2.0407 5 403.0 14.70 389.61 1.92 50.00 164 | 1.51902 0.00 19.580 1 0.6050 8.3750 93.90 2.1620 5 403.0 14.70 388.45 3.32 50.00 165 | 2.24236 0.00 19.580 0 0.6050 5.8540 91.80 2.4220 5 403.0 14.70 395.11 11.64 22.70 166 | 2.92400 0.00 19.580 0 0.6050 6.1010 93.00 2.2834 5 403.0 14.70 240.16 9.81 25.00 167 | 2.01019 0.00 19.580 0 0.6050 7.9290 96.20 2.0459 5 403.0 14.70 369.30 3.70 50.00 168 | 1.80028 0.00 19.580 0 0.6050 5.8770 79.20 2.4259 5 403.0 14.70 227.61 12.14 23.80 169 | 2.30040 0.00 19.580 0 0.6050 6.3190 96.10 2.1000 5 403.0 14.70 297.09 11.10 23.80 170 | 2.44953 0.00 19.580 0 0.6050 6.4020 95.20 2.2625 5 403.0 14.70 330.04 11.32 22.30 171 | 1.20742 0.00 19.580 0 0.6050 5.8750 94.60 2.4259 5 403.0 14.70 292.29 14.43 17.40 172 | 2.31390 0.00 19.580 0 0.6050 5.8800 97.30 2.3887 5 403.0 14.70 348.13 12.03 19.10 173 | 0.13914 0.00 4.050 0 0.5100 5.5720 88.50 2.5961 5 296.0 16.60 396.90 14.69 23.10 174 | 0.09178 0.00 4.050 0 0.5100 6.4160 84.10 2.6463 5 296.0 16.60 395.50 9.04 23.60 175 | 0.08447 0.00 4.050 0 0.5100 5.8590 68.70 2.7019 5 296.0 16.60 393.23 9.64 22.60 176 | 0.06664 0.00 4.050 0 0.5100 6.5460 33.10 3.1323 5 296.0 16.60 390.96 5.33 29.40 177 | 0.07022 0.00 4.050 0 0.5100 6.0200 47.20 3.5549 5 296.0 16.60 393.23 10.11 23.20 178 | 0.05425 0.00 4.050 0 0.5100 6.3150 73.40 3.3175 5 296.0 16.60 395.60 6.29 24.60 179 | 0.06642 0.00 4.050 0 0.5100 6.8600 74.40 2.9153 5 296.0 16.60 391.27 6.92 29.90 180 | 0.05780 0.00 2.460 0 0.4880 6.9800 58.40 2.8290 3 193.0 17.80 396.90 5.04 37.20 181 | 0.06588 0.00 2.460 0 0.4880 7.7650 83.30 2.7410 3 193.0 17.80 395.56 7.56 39.80 182 | 0.06888 0.00 2.460 0 0.4880 6.1440 62.20 2.5979 3 193.0 17.80 396.90 9.45 36.20 183 | 0.09103 0.00 2.460 0 0.4880 7.1550 92.20 2.7006 3 193.0 17.80 394.12 4.82 37.90 184 | 0.10008 0.00 2.460 0 0.4880 6.5630 95.60 2.8470 3 193.0 17.80 396.90 5.68 32.50 185 | 0.08308 0.00 2.460 0 0.4880 5.6040 89.80 2.9879 3 193.0 17.80 391.00 13.98 26.40 186 | 0.06047 0.00 2.460 0 0.4880 6.1530 68.80 3.2797 3 193.0 17.80 387.11 13.15 29.60 187 | 0.05602 0.00 2.460 0 0.4880 7.8310 53.60 3.1992 3 193.0 17.80 392.63 4.45 50.00 188 | 0.07875 45.00 3.440 0 0.4370 6.7820 41.10 3.7886 5 398.0 15.20 393.87 6.68 32.00 189 | 0.12579 45.00 3.440 0 0.4370 6.5560 29.10 4.5667 5 398.0 15.20 382.84 4.56 29.80 190 | 0.08370 45.00 3.440 0 0.4370 7.1850 38.90 4.5667 5 398.0 15.20 396.90 5.39 34.90 191 | 0.09068 45.00 3.440 0 0.4370 6.9510 21.50 6.4798 5 398.0 15.20 377.68 5.10 37.00 192 | 0.06911 45.00 3.440 0 0.4370 6.7390 30.80 6.4798 5 398.0 15.20 389.71 4.69 30.50 193 | 0.08664 45.00 3.440 0 0.4370 7.1780 26.30 6.4798 5 398.0 15.20 390.49 2.87 36.40 194 | 0.02187 60.00 2.930 0 0.4010 6.8000 9.90 6.2196 1 265.0 15.60 393.37 5.03 31.10 195 | 0.01439 60.00 2.930 0 0.4010 6.6040 18.80 6.2196 1 265.0 15.60 376.70 4.38 29.10 196 | 0.01381 80.00 0.460 0 0.4220 7.8750 32.00 5.6484 4 255.0 14.40 394.23 2.97 50.00 197 | 0.04011 80.00 1.520 0 0.4040 7.2870 34.10 7.3090 2 329.0 12.60 396.90 4.08 33.30 198 | 0.04666 80.00 1.520 0 0.4040 7.1070 36.60 7.3090 2 329.0 12.60 354.31 8.61 30.30 199 | 0.03768 80.00 1.520 0 0.4040 7.2740 38.30 7.3090 2 329.0 12.60 392.20 6.62 34.60 200 | 0.03150 95.00 1.470 0 0.4030 6.9750 15.30 7.6534 3 402.0 17.00 396.90 4.56 34.90 201 | 0.01778 95.00 1.470 0 0.4030 7.1350 13.90 7.6534 3 402.0 17.00 384.30 4.45 32.90 202 | 0.03445 82.50 2.030 0 0.4150 6.1620 38.40 6.2700 2 348.0 14.70 393.77 7.43 24.10 203 | 0.02177 82.50 2.030 0 0.4150 7.6100 15.70 6.2700 2 348.0 14.70 395.38 3.11 42.30 204 | 0.03510 95.00 2.680 0 0.4161 7.8530 33.20 5.1180 4 224.0 14.70 392.78 3.81 48.50 205 | 0.02009 95.00 2.680 0 0.4161 8.0340 31.90 5.1180 4 224.0 14.70 390.55 2.88 50.00 206 | 0.13642 0.00 10.590 0 0.4890 5.8910 22.30 3.9454 4 277.0 18.60 396.90 10.87 22.60 207 | 0.22969 0.00 10.590 0 0.4890 6.3260 52.50 4.3549 4 277.0 18.60 394.87 10.97 24.40 208 | 0.25199 0.00 10.590 0 0.4890 5.7830 72.70 4.3549 4 277.0 18.60 389.43 18.06 22.50 209 | 0.13587 0.00 10.590 1 0.4890 6.0640 59.10 4.2392 4 277.0 18.60 381.32 14.66 24.40 210 | 0.43571 0.00 10.590 1 0.4890 5.3440 100.00 3.8750 4 277.0 18.60 396.90 23.09 20.00 211 | 0.17446 0.00 10.590 1 0.4890 5.9600 92.10 3.8771 4 277.0 18.60 393.25 17.27 21.70 212 | 0.37578 0.00 10.590 1 0.4890 5.4040 88.60 3.6650 4 277.0 18.60 395.24 23.98 19.30 213 | 0.21719 0.00 10.590 1 0.4890 5.8070 53.80 3.6526 4 277.0 18.60 390.94 16.03 22.40 214 | 0.14052 0.00 10.590 0 0.4890 6.3750 32.30 3.9454 4 277.0 18.60 385.81 9.38 28.10 215 | 0.28955 0.00 10.590 0 0.4890 5.4120 9.80 3.5875 4 277.0 18.60 348.93 29.55 23.70 216 | 0.19802 0.00 10.590 0 0.4890 6.1820 42.40 3.9454 4 277.0 18.60 393.63 9.47 25.00 217 | 0.04560 0.00 13.890 1 0.5500 5.8880 56.00 3.1121 5 276.0 16.40 392.80 13.51 23.30 218 | 0.07013 0.00 13.890 0 0.5500 6.6420 85.10 3.4211 5 276.0 16.40 392.78 9.69 28.70 219 | 0.11069 0.00 13.890 1 0.5500 5.9510 93.80 2.8893 5 276.0 16.40 396.90 17.92 21.50 220 | 0.11425 0.00 13.890 1 0.5500 6.3730 92.40 3.3633 5 276.0 16.40 393.74 10.50 23.00 221 | 0.35809 0.00 6.200 1 0.5070 6.9510 88.50 2.8617 8 307.0 17.40 391.70 9.71 26.70 222 | 0.40771 0.00 6.200 1 0.5070 6.1640 91.30 3.0480 8 307.0 17.40 395.24 21.46 21.70 223 | 0.62356 0.00 6.200 1 0.5070 6.8790 77.70 3.2721 8 307.0 17.40 390.39 9.93 27.50 224 | 0.61470 0.00 6.200 0 0.5070 6.6180 80.80 3.2721 8 307.0 17.40 396.90 7.60 30.10 225 | 0.31533 0.00 6.200 0 0.5040 8.2660 78.30 2.8944 8 307.0 17.40 385.05 4.14 44.80 226 | 0.52693 0.00 6.200 0 0.5040 8.7250 83.00 2.8944 8 307.0 17.40 382.00 4.63 50.00 227 | 0.38214 0.00 6.200 0 0.5040 8.0400 86.50 3.2157 8 307.0 17.40 387.38 3.13 37.60 228 | 0.41238 0.00 6.200 0 0.5040 7.1630 79.90 3.2157 8 307.0 17.40 372.08 6.36 31.60 229 | 0.29819 0.00 6.200 0 0.5040 7.6860 17.00 3.3751 8 307.0 17.40 377.51 3.92 46.70 230 | 0.44178 0.00 6.200 0 0.5040 6.5520 21.40 3.3751 8 307.0 17.40 380.34 3.76 31.50 231 | 0.53700 0.00 6.200 0 0.5040 5.9810 68.10 3.6715 8 307.0 17.40 378.35 11.65 24.30 232 | 0.46296 0.00 6.200 0 0.5040 7.4120 76.90 3.6715 8 307.0 17.40 376.14 5.25 31.70 233 | 0.57529 0.00 6.200 0 0.5070 8.3370 73.30 3.8384 8 307.0 17.40 385.91 2.47 41.70 234 | 0.33147 0.00 6.200 0 0.5070 8.2470 70.40 3.6519 8 307.0 17.40 378.95 3.95 48.30 235 | 0.44791 0.00 6.200 1 0.5070 6.7260 66.50 3.6519 8 307.0 17.40 360.20 8.05 29.00 236 | 0.33045 0.00 6.200 0 0.5070 6.0860 61.50 3.6519 8 307.0 17.40 376.75 10.88 24.00 237 | 0.52058 0.00 6.200 1 0.5070 6.6310 76.50 4.1480 8 307.0 17.40 388.45 9.54 25.10 238 | 0.51183 0.00 6.200 0 0.5070 7.3580 71.60 4.1480 8 307.0 17.40 390.07 4.73 31.50 239 | 0.08244 30.00 4.930 0 0.4280 6.4810 18.50 6.1899 6 300.0 16.60 379.41 6.36 23.70 240 | 0.09252 30.00 4.930 0 0.4280 6.6060 42.20 6.1899 6 300.0 16.60 383.78 7.37 23.30 241 | 0.11329 30.00 4.930 0 0.4280 6.8970 54.30 6.3361 6 300.0 16.60 391.25 11.38 22.00 242 | 0.10612 30.00 4.930 0 0.4280 6.0950 65.10 6.3361 6 300.0 16.60 394.62 12.40 20.10 243 | 0.10290 30.00 4.930 0 0.4280 6.3580 52.90 7.0355 6 300.0 16.60 372.75 11.22 22.20 244 | 0.12757 30.00 4.930 0 0.4280 6.3930 7.80 7.0355 6 300.0 16.60 374.71 5.19 23.70 245 | 0.20608 22.00 5.860 0 0.4310 5.5930 76.50 7.9549 7 330.0 19.10 372.49 12.50 17.60 246 | 0.19133 22.00 5.860 0 0.4310 5.6050 70.20 7.9549 7 330.0 19.10 389.13 18.46 18.50 247 | 0.33983 22.00 5.860 0 0.4310 6.1080 34.90 8.0555 7 330.0 19.10 390.18 9.16 24.30 248 | 0.19657 22.00 5.860 0 0.4310 6.2260 79.20 8.0555 7 330.0 19.10 376.14 10.15 20.50 249 | 0.16439 22.00 5.860 0 0.4310 6.4330 49.10 7.8265 7 330.0 19.10 374.71 9.52 24.50 250 | 0.19073 22.00 5.860 0 0.4310 6.7180 17.50 7.8265 7 330.0 19.10 393.74 6.56 26.20 251 | 0.14030 22.00 5.860 0 0.4310 6.4870 13.00 7.3967 7 330.0 19.10 396.28 5.90 24.40 252 | 0.21409 22.00 5.860 0 0.4310 6.4380 8.90 7.3967 7 330.0 19.10 377.07 3.59 24.80 253 | 0.08221 22.00 5.860 0 0.4310 6.9570 6.80 8.9067 7 330.0 19.10 386.09 3.53 29.60 254 | 0.36894 22.00 5.860 0 0.4310 8.2590 8.40 8.9067 7 330.0 19.10 396.90 3.54 42.80 255 | 0.04819 80.00 3.640 0 0.3920 6.1080 32.00 9.2203 1 315.0 16.40 392.89 6.57 21.90 256 | 0.03548 80.00 3.640 0 0.3920 5.8760 19.10 9.2203 1 315.0 16.40 395.18 9.25 20.90 257 | 0.01538 90.00 3.750 0 0.3940 7.4540 34.20 6.3361 3 244.0 15.90 386.34 3.11 44.00 258 | 0.61154 20.00 3.970 0 0.6470 8.7040 86.90 1.8010 5 264.0 13.00 389.70 5.12 50.00 259 | 0.66351 20.00 3.970 0 0.6470 7.3330 100.00 1.8946 5 264.0 13.00 383.29 7.79 36.00 260 | 0.65665 20.00 3.970 0 0.6470 6.8420 100.00 2.0107 5 264.0 13.00 391.93 6.90 30.10 261 | 0.54011 20.00 3.970 0 0.6470 7.2030 81.80 2.1121 5 264.0 13.00 392.80 9.59 33.80 262 | 0.53412 20.00 3.970 0 0.6470 7.5200 89.40 2.1398 5 264.0 13.00 388.37 7.26 43.10 263 | 0.52014 20.00 3.970 0 0.6470 8.3980 91.50 2.2885 5 264.0 13.00 386.86 5.91 48.80 264 | 0.82526 20.00 3.970 0 0.6470 7.3270 94.50 2.0788 5 264.0 13.00 393.42 11.25 31.00 265 | 0.55007 20.00 3.970 0 0.6470 7.2060 91.60 1.9301 5 264.0 13.00 387.89 8.10 36.50 266 | 0.76162 20.00 3.970 0 0.6470 5.5600 62.80 1.9865 5 264.0 13.00 392.40 10.45 22.80 267 | 0.78570 20.00 3.970 0 0.6470 7.0140 84.60 2.1329 5 264.0 13.00 384.07 14.79 30.70 268 | 0.57834 20.00 3.970 0 0.5750 8.2970 67.00 2.4216 5 264.0 13.00 384.54 7.44 50.00 269 | 0.54050 20.00 3.970 0 0.5750 7.4700 52.60 2.8720 5 264.0 13.00 390.30 3.16 43.50 270 | 0.09065 20.00 6.960 1 0.4640 5.9200 61.50 3.9175 3 223.0 18.60 391.34 13.65 20.70 271 | 0.29916 20.00 6.960 0 0.4640 5.8560 42.10 4.4290 3 223.0 18.60 388.65 13.00 21.10 272 | 0.16211 20.00 6.960 0 0.4640 6.2400 16.30 4.4290 3 223.0 18.60 396.90 6.59 25.20 273 | 0.11460 20.00 6.960 0 0.4640 6.5380 58.70 3.9175 3 223.0 18.60 394.96 7.73 24.40 274 | 0.22188 20.00 6.960 1 0.4640 7.6910 51.80 4.3665 3 223.0 18.60 390.77 6.58 35.20 275 | 0.05644 40.00 6.410 1 0.4470 6.7580 32.90 4.0776 4 254.0 17.60 396.90 3.53 32.40 276 | 0.09604 40.00 6.410 0 0.4470 6.8540 42.80 4.2673 4 254.0 17.60 396.90 2.98 32.00 277 | 0.10469 40.00 6.410 1 0.4470 7.2670 49.00 4.7872 4 254.0 17.60 389.25 6.05 33.20 278 | 0.06127 40.00 6.410 1 0.4470 6.8260 27.60 4.8628 4 254.0 17.60 393.45 4.16 33.10 279 | 0.07978 40.00 6.410 0 0.4470 6.4820 32.10 4.1403 4 254.0 17.60 396.90 7.19 29.10 280 | 0.21038 20.00 3.330 0 0.4429 6.8120 32.20 4.1007 5 216.0 14.90 396.90 4.85 35.10 281 | 0.03578 20.00 3.330 0 0.4429 7.8200 64.50 4.6947 5 216.0 14.90 387.31 3.76 45.40 282 | 0.03705 20.00 3.330 0 0.4429 6.9680 37.20 5.2447 5 216.0 14.90 392.23 4.59 35.40 283 | 0.06129 20.00 3.330 1 0.4429 7.6450 49.70 5.2119 5 216.0 14.90 377.07 3.01 46.00 284 | 0.01501 90.00 1.210 1 0.4010 7.9230 24.80 5.8850 1 198.0 13.60 395.52 3.16 50.00 285 | 0.00906 90.00 2.970 0 0.4000 7.0880 20.80 7.3073 1 285.0 15.30 394.72 7.85 32.20 286 | 0.01096 55.00 2.250 0 0.3890 6.4530 31.90 7.3073 1 300.0 15.30 394.72 8.23 22.00 287 | 0.01965 80.00 1.760 0 0.3850 6.2300 31.50 9.0892 1 241.0 18.20 341.60 12.93 20.10 288 | 0.03871 52.50 5.320 0 0.4050 6.2090 31.30 7.3172 6 293.0 16.60 396.90 7.14 23.20 289 | 0.04590 52.50 5.320 0 0.4050 6.3150 45.60 7.3172 6 293.0 16.60 396.90 7.60 22.30 290 | 0.04297 52.50 5.320 0 0.4050 6.5650 22.90 7.3172 6 293.0 16.60 371.72 9.51 24.80 291 | 0.03502 80.00 4.950 0 0.4110 6.8610 27.90 5.1167 4 245.0 19.20 396.90 3.33 28.50 292 | 0.07886 80.00 4.950 0 0.4110 7.1480 27.70 5.1167 4 245.0 19.20 396.90 3.56 37.30 293 | 0.03615 80.00 4.950 0 0.4110 6.6300 23.40 5.1167 4 245.0 19.20 396.90 4.70 27.90 294 | 0.08265 0.00 13.920 0 0.4370 6.1270 18.40 5.5027 4 289.0 16.00 396.90 8.58 23.90 295 | 0.08199 0.00 13.920 0 0.4370 6.0090 42.30 5.5027 4 289.0 16.00 396.90 10.40 21.70 296 | 0.12932 0.00 13.920 0 0.4370 6.6780 31.10 5.9604 4 289.0 16.00 396.90 6.27 28.60 297 | 0.05372 0.00 13.920 0 0.4370 6.5490 51.00 5.9604 4 289.0 16.00 392.85 7.39 27.10 298 | 0.14103 0.00 13.920 0 0.4370 5.7900 58.00 6.3200 4 289.0 16.00 396.90 15.84 20.30 299 | 0.06466 70.00 2.240 0 0.4000 6.3450 20.10 7.8278 5 358.0 14.80 368.24 4.97 22.50 300 | 0.05561 70.00 2.240 0 0.4000 7.0410 10.00 7.8278 5 358.0 14.80 371.58 4.74 29.00 301 | 0.04417 70.00 2.240 0 0.4000 6.8710 47.40 7.8278 5 358.0 14.80 390.86 6.07 24.80 302 | 0.03537 34.00 6.090 0 0.4330 6.5900 40.40 5.4917 7 329.0 16.10 395.75 9.50 22.00 303 | 0.09266 34.00 6.090 0 0.4330 6.4950 18.40 5.4917 7 329.0 16.10 383.61 8.67 26.40 304 | 0.10000 34.00 6.090 0 0.4330 6.9820 17.70 5.4917 7 329.0 16.10 390.43 4.86 33.10 305 | 0.05515 33.00 2.180 0 0.4720 7.2360 41.10 4.0220 7 222.0 18.40 393.68 6.93 36.10 306 | 0.05479 33.00 2.180 0 0.4720 6.6160 58.10 3.3700 7 222.0 18.40 393.36 8.93 28.40 307 | 0.07503 33.00 2.180 0 0.4720 7.4200 71.90 3.0992 7 222.0 18.40 396.90 6.47 33.40 308 | 0.04932 33.00 2.180 0 0.4720 6.8490 70.30 3.1827 7 222.0 18.40 396.90 7.53 28.20 309 | 0.49298 0.00 9.900 0 0.5440 6.6350 82.50 3.3175 4 304.0 18.40 396.90 4.54 22.80 310 | 0.34940 0.00 9.900 0 0.5440 5.9720 76.70 3.1025 4 304.0 18.40 396.24 9.97 20.30 311 | 2.63548 0.00 9.900 0 0.5440 4.9730 37.80 2.5194 4 304.0 18.40 350.45 12.64 16.10 312 | 0.79041 0.00 9.900 0 0.5440 6.1220 52.80 2.6403 4 304.0 18.40 396.90 5.98 22.10 313 | 0.26169 0.00 9.900 0 0.5440 6.0230 90.40 2.8340 4 304.0 18.40 396.30 11.72 19.40 314 | 0.26938 0.00 9.900 0 0.5440 6.2660 82.80 3.2628 4 304.0 18.40 393.39 7.90 21.60 315 | 0.36920 0.00 9.900 0 0.5440 6.5670 87.30 3.6023 4 304.0 18.40 395.69 9.28 23.80 316 | 0.25356 0.00 9.900 0 0.5440 5.7050 77.70 3.9450 4 304.0 18.40 396.42 11.50 16.20 317 | 0.31827 0.00 9.900 0 0.5440 5.9140 83.20 3.9986 4 304.0 18.40 390.70 18.33 17.80 318 | 0.24522 0.00 9.900 0 0.5440 5.7820 71.70 4.0317 4 304.0 18.40 396.90 15.94 19.80 319 | 0.40202 0.00 9.900 0 0.5440 6.3820 67.20 3.5325 4 304.0 18.40 395.21 10.36 23.10 320 | 0.47547 0.00 9.900 0 0.5440 6.1130 58.80 4.0019 4 304.0 18.40 396.23 12.73 21.00 321 | 0.16760 0.00 7.380 0 0.4930 6.4260 52.30 4.5404 5 287.0 19.60 396.90 7.20 23.80 322 | 0.18159 0.00 7.380 0 0.4930 6.3760 54.30 4.5404 5 287.0 19.60 396.90 6.87 23.10 323 | 0.35114 0.00 7.380 0 0.4930 6.0410 49.90 4.7211 5 287.0 19.60 396.90 7.70 20.40 324 | 0.28392 0.00 7.380 0 0.4930 5.7080 74.30 4.7211 5 287.0 19.60 391.13 11.74 18.50 325 | 0.34109 0.00 7.380 0 0.4930 6.4150 40.10 4.7211 5 287.0 19.60 396.90 6.12 25.00 326 | 0.19186 0.00 7.380 0 0.4930 6.4310 14.70 5.4159 5 287.0 19.60 393.68 5.08 24.60 327 | 0.30347 0.00 7.380 0 0.4930 6.3120 28.90 5.4159 5 287.0 19.60 396.90 6.15 23.00 328 | 0.24103 0.00 7.380 0 0.4930 6.0830 43.70 5.4159 5 287.0 19.60 396.90 12.79 22.20 329 | 0.06617 0.00 3.240 0 0.4600 5.8680 25.80 5.2146 4 430.0 16.90 382.44 9.97 19.30 330 | 0.06724 0.00 3.240 0 0.4600 6.3330 17.20 5.2146 4 430.0 16.90 375.21 7.34 22.60 331 | 0.04544 0.00 3.240 0 0.4600 6.1440 32.20 5.8736 4 430.0 16.90 368.57 9.09 19.80 332 | 0.05023 35.00 6.060 0 0.4379 5.7060 28.40 6.6407 1 304.0 16.90 394.02 12.43 17.10 333 | 0.03466 35.00 6.060 0 0.4379 6.0310 23.30 6.6407 1 304.0 16.90 362.25 7.83 19.40 334 | 0.05083 0.00 5.190 0 0.5150 6.3160 38.10 6.4584 5 224.0 20.20 389.71 5.68 22.20 335 | 0.03738 0.00 5.190 0 0.5150 6.3100 38.50 6.4584 5 224.0 20.20 389.40 6.75 20.70 336 | 0.03961 0.00 5.190 0 0.5150 6.0370 34.50 5.9853 5 224.0 20.20 396.90 8.01 21.10 337 | 0.03427 0.00 5.190 0 0.5150 5.8690 46.30 5.2311 5 224.0 20.20 396.90 9.80 19.50 338 | 0.03041 0.00 5.190 0 0.5150 5.8950 59.60 5.6150 5 224.0 20.20 394.81 10.56 18.50 339 | 0.03306 0.00 5.190 0 0.5150 6.0590 37.30 4.8122 5 224.0 20.20 396.14 8.51 20.60 340 | 0.05497 0.00 5.190 0 0.5150 5.9850 45.40 4.8122 5 224.0 20.20 396.90 9.74 19.00 341 | 0.06151 0.00 5.190 0 0.5150 5.9680 58.50 4.8122 5 224.0 20.20 396.90 9.29 18.70 342 | 0.01301 35.00 1.520 0 0.4420 7.2410 49.30 7.0379 1 284.0 15.50 394.74 5.49 32.70 343 | 0.02498 0.00 1.890 0 0.5180 6.5400 59.70 6.2669 1 422.0 15.90 389.96 8.65 16.50 344 | 0.02543 55.00 3.780 0 0.4840 6.6960 56.40 5.7321 5 370.0 17.60 396.90 7.18 23.90 345 | 0.03049 55.00 3.780 0 0.4840 6.8740 28.10 6.4654 5 370.0 17.60 387.97 4.61 31.20 346 | 0.03113 0.00 4.390 0 0.4420 6.0140 48.50 8.0136 3 352.0 18.80 385.64 10.53 17.50 347 | 0.06162 0.00 4.390 0 0.4420 5.8980 52.30 8.0136 3 352.0 18.80 364.61 12.67 17.20 348 | 0.01870 85.00 4.150 0 0.4290 6.5160 27.70 8.5353 4 351.0 17.90 392.43 6.36 23.10 349 | 0.01501 80.00 2.010 0 0.4350 6.6350 29.70 8.3440 4 280.0 17.00 390.94 5.99 24.50 350 | 0.02899 40.00 1.250 0 0.4290 6.9390 34.50 8.7921 1 335.0 19.70 389.85 5.89 26.60 351 | 0.06211 40.00 1.250 0 0.4290 6.4900 44.40 8.7921 1 335.0 19.70 396.90 5.98 22.90 352 | 0.07950 60.00 1.690 0 0.4110 6.5790 35.90 10.7103 4 411.0 18.30 370.78 5.49 24.10 353 | 0.07244 60.00 1.690 0 0.4110 5.8840 18.50 10.7103 4 411.0 18.30 392.33 7.79 18.60 354 | 0.01709 90.00 2.020 0 0.4100 6.7280 36.10 12.1265 5 187.0 17.00 384.46 4.50 30.10 355 | 0.04301 80.00 1.910 0 0.4130 5.6630 21.90 10.5857 4 334.0 22.00 382.80 8.05 18.20 356 | 0.10659 80.00 1.910 0 0.4130 5.9360 19.50 10.5857 4 334.0 22.00 376.04 5.57 20.60 357 | 8.98296 0.00 18.100 1 0.7700 6.2120 97.40 2.1222 24 666.0 20.20 377.73 17.60 17.80 358 | 3.84970 0.00 18.100 1 0.7700 6.3950 91.00 2.5052 24 666.0 20.20 391.34 13.27 21.70 359 | 5.20177 0.00 18.100 1 0.7700 6.1270 83.40 2.7227 24 666.0 20.20 395.43 11.48 22.70 360 | 4.26131 0.00 18.100 0 0.7700 6.1120 81.30 2.5091 24 666.0 20.20 390.74 12.67 22.60 361 | 4.54192 0.00 18.100 0 0.7700 6.3980 88.00 2.5182 24 666.0 20.20 374.56 7.79 25.00 362 | 3.83684 0.00 18.100 0 0.7700 6.2510 91.10 2.2955 24 666.0 20.20 350.65 14.19 19.90 363 | 3.67822 0.00 18.100 0 0.7700 5.3620 96.20 2.1036 24 666.0 20.20 380.79 10.19 20.80 364 | 4.22239 0.00 18.100 1 0.7700 5.8030 89.00 1.9047 24 666.0 20.20 353.04 14.64 16.80 365 | 3.47428 0.00 18.100 1 0.7180 8.7800 82.90 1.9047 24 666.0 20.20 354.55 5.29 21.90 366 | 4.55587 0.00 18.100 0 0.7180 3.5610 87.90 1.6132 24 666.0 20.20 354.70 7.12 27.50 367 | 3.69695 0.00 18.100 0 0.7180 4.9630 91.40 1.7523 24 666.0 20.20 316.03 14.00 21.90 368 | 13.52220 0.00 18.100 0 0.6310 3.8630 100.00 1.5106 24 666.0 20.20 131.42 13.33 23.10 369 | 4.89822 0.00 18.100 0 0.6310 4.9700 100.00 1.3325 24 666.0 20.20 375.52 3.26 50.00 370 | 5.66998 0.00 18.100 1 0.6310 6.6830 96.80 1.3567 24 666.0 20.20 375.33 3.73 50.00 371 | 6.53876 0.00 18.100 1 0.6310 7.0160 97.50 1.2024 24 666.0 20.20 392.05 2.96 50.00 372 | 9.23230 0.00 18.100 0 0.6310 6.2160 100.00 1.1691 24 666.0 20.20 366.15 9.53 50.00 373 | 8.26725 0.00 18.100 1 0.6680 5.8750 89.60 1.1296 24 666.0 20.20 347.88 8.88 50.00 374 | 11.10810 0.00 18.100 0 0.6680 4.9060 100.00 1.1742 24 666.0 20.20 396.90 34.77 13.80 375 | 18.49820 0.00 18.100 0 0.6680 4.1380 100.00 1.1370 24 666.0 20.20 396.90 37.97 13.80 376 | 19.60910 0.00 18.100 0 0.6710 7.3130 97.90 1.3163 24 666.0 20.20 396.90 13.44 15.00 377 | 15.28800 0.00 18.100 0 0.6710 6.6490 93.30 1.3449 24 666.0 20.20 363.02 23.24 13.90 378 | 9.82349 0.00 18.100 0 0.6710 6.7940 98.80 1.3580 24 666.0 20.20 396.90 21.24 13.30 379 | 23.64820 0.00 18.100 0 0.6710 6.3800 96.20 1.3861 24 666.0 20.20 396.90 23.69 13.10 380 | 17.86670 0.00 18.100 0 0.6710 6.2230 100.00 1.3861 24 666.0 20.20 393.74 21.78 10.20 381 | 88.97620 0.00 18.100 0 0.6710 6.9680 91.90 1.4165 24 666.0 20.20 396.90 17.21 10.40 382 | 15.87440 0.00 18.100 0 0.6710 6.5450 99.10 1.5192 24 666.0 20.20 396.90 21.08 10.90 383 | 9.18702 0.00 18.100 0 0.7000 5.5360 100.00 1.5804 24 666.0 20.20 396.90 23.60 11.30 384 | 7.99248 0.00 18.100 0 0.7000 5.5200 100.00 1.5331 24 666.0 20.20 396.90 24.56 12.30 385 | 20.08490 0.00 18.100 0 0.7000 4.3680 91.20 1.4395 24 666.0 20.20 285.83 30.63 8.80 386 | 16.81180 0.00 18.100 0 0.7000 5.2770 98.10 1.4261 24 666.0 20.20 396.90 30.81 7.20 387 | 24.39380 0.00 18.100 0 0.7000 4.6520 100.00 1.4672 24 666.0 20.20 396.90 28.28 10.50 388 | 22.59710 0.00 18.100 0 0.7000 5.0000 89.50 1.5184 24 666.0 20.20 396.90 31.99 7.40 389 | 14.33370 0.00 18.100 0 0.7000 4.8800 100.00 1.5895 24 666.0 20.20 372.92 30.62 10.20 390 | 8.15174 0.00 18.100 0 0.7000 5.3900 98.90 1.7281 24 666.0 20.20 396.90 20.85 11.50 391 | 6.96215 0.00 18.100 0 0.7000 5.7130 97.00 1.9265 24 666.0 20.20 394.43 17.11 15.10 392 | 5.29305 0.00 18.100 0 0.7000 6.0510 82.50 2.1678 24 666.0 20.20 378.38 18.76 23.20 393 | 11.57790 0.00 18.100 0 0.7000 5.0360 97.00 1.7700 24 666.0 20.20 396.90 25.68 9.70 394 | 8.64476 0.00 18.100 0 0.6930 6.1930 92.60 1.7912 24 666.0 20.20 396.90 15.17 13.80 395 | 13.35980 0.00 18.100 0 0.6930 5.8870 94.70 1.7821 24 666.0 20.20 396.90 16.35 12.70 396 | 8.71675 0.00 18.100 0 0.6930 6.4710 98.80 1.7257 24 666.0 20.20 391.98 17.12 13.10 397 | 5.87205 0.00 18.100 0 0.6930 6.4050 96.00 1.6768 24 666.0 20.20 396.90 19.37 12.50 398 | 7.67202 0.00 18.100 0 0.6930 5.7470 98.90 1.6334 24 666.0 20.20 393.10 19.92 8.50 399 | 38.35180 0.00 18.100 0 0.6930 5.4530 100.00 1.4896 24 666.0 20.20 396.90 30.59 5.00 400 | 9.91655 0.00 18.100 0 0.6930 5.8520 77.80 1.5004 24 666.0 20.20 338.16 29.97 6.30 401 | 25.04610 0.00 18.100 0 0.6930 5.9870 100.00 1.5888 24 666.0 20.20 396.90 26.77 5.60 402 | 14.23620 0.00 18.100 0 0.6930 6.3430 100.00 1.5741 24 666.0 20.20 396.90 20.32 7.20 403 | 9.59571 0.00 18.100 0 0.6930 6.4040 100.00 1.6390 24 666.0 20.20 376.11 20.31 12.10 404 | 24.80170 0.00 18.100 0 0.6930 5.3490 96.00 1.7028 24 666.0 20.20 396.90 19.77 8.30 405 | 41.52920 0.00 18.100 0 0.6930 5.5310 85.40 1.6074 24 666.0 20.20 329.46 27.38 8.50 406 | 67.92080 0.00 18.100 0 0.6930 5.6830 100.00 1.4254 24 666.0 20.20 384.97 22.98 5.00 407 | 20.71620 0.00 18.100 0 0.6590 4.1380 100.00 1.1781 24 666.0 20.20 370.22 23.34 11.90 408 | 11.95110 0.00 18.100 0 0.6590 5.6080 100.00 1.2852 24 666.0 20.20 332.09 12.13 27.90 409 | 7.40389 0.00 18.100 0 0.5970 5.6170 97.90 1.4547 24 666.0 20.20 314.64 26.40 17.20 410 | 14.43830 0.00 18.100 0 0.5970 6.8520 100.00 1.4655 24 666.0 20.20 179.36 19.78 27.50 411 | 51.13580 0.00 18.100 0 0.5970 5.7570 100.00 1.4130 24 666.0 20.20 2.60 10.11 15.00 412 | 14.05070 0.00 18.100 0 0.5970 6.6570 100.00 1.5275 24 666.0 20.20 35.05 21.22 17.20 413 | 18.81100 0.00 18.100 0 0.5970 4.6280 100.00 1.5539 24 666.0 20.20 28.79 34.37 17.90 414 | 28.65580 0.00 18.100 0 0.5970 5.1550 100.00 1.5894 24 666.0 20.20 210.97 20.08 16.30 415 | 45.74610 0.00 18.100 0 0.6930 4.5190 100.00 1.6582 24 666.0 20.20 88.27 36.98 7.00 416 | 18.08460 0.00 18.100 0 0.6790 6.4340 100.00 1.8347 24 666.0 20.20 27.25 29.05 7.20 417 | 10.83420 0.00 18.100 0 0.6790 6.7820 90.80 1.8195 24 666.0 20.20 21.57 25.79 7.50 418 | 25.94060 0.00 18.100 0 0.6790 5.3040 89.10 1.6475 24 666.0 20.20 127.36 26.64 10.40 419 | 73.53410 0.00 18.100 0 0.6790 5.9570 100.00 1.8026 24 666.0 20.20 16.45 20.62 8.80 420 | 11.81230 0.00 18.100 0 0.7180 6.8240 76.50 1.7940 24 666.0 20.20 48.45 22.74 8.40 421 | 11.08740 0.00 18.100 0 0.7180 6.4110 100.00 1.8589 24 666.0 20.20 318.75 15.02 16.70 422 | 7.02259 0.00 18.100 0 0.7180 6.0060 95.30 1.8746 24 666.0 20.20 319.98 15.70 14.20 423 | 12.04820 0.00 18.100 0 0.6140 5.6480 87.60 1.9512 24 666.0 20.20 291.55 14.10 20.80 424 | 7.05042 0.00 18.100 0 0.6140 6.1030 85.10 2.0218 24 666.0 20.20 2.52 23.29 13.40 425 | 8.79212 0.00 18.100 0 0.5840 5.5650 70.60 2.0635 24 666.0 20.20 3.65 17.16 11.70 426 | 15.86030 0.00 18.100 0 0.6790 5.8960 95.40 1.9096 24 666.0 20.20 7.68 24.39 8.30 427 | 12.24720 0.00 18.100 0 0.5840 5.8370 59.70 1.9976 24 666.0 20.20 24.65 15.69 10.20 428 | 37.66190 0.00 18.100 0 0.6790 6.2020 78.70 1.8629 24 666.0 20.20 18.82 14.52 10.90 429 | 7.36711 0.00 18.100 0 0.6790 6.1930 78.10 1.9356 24 666.0 20.20 96.73 21.52 11.00 430 | 9.33889 0.00 18.100 0 0.6790 6.3800 95.60 1.9682 24 666.0 20.20 60.72 24.08 9.50 431 | 8.49213 0.00 18.100 0 0.5840 6.3480 86.10 2.0527 24 666.0 20.20 83.45 17.64 14.50 432 | 10.06230 0.00 18.100 0 0.5840 6.8330 94.30 2.0882 24 666.0 20.20 81.33 19.69 14.10 433 | 6.44405 0.00 18.100 0 0.5840 6.4250 74.80 2.2004 24 666.0 20.20 97.95 12.03 16.10 434 | 5.58107 0.00 18.100 0 0.7130 6.4360 87.90 2.3158 24 666.0 20.20 100.19 16.22 14.30 435 | 13.91340 0.00 18.100 0 0.7130 6.2080 95.00 2.2222 24 666.0 20.20 100.63 15.17 11.70 436 | 11.16040 0.00 18.100 0 0.7400 6.6290 94.60 2.1247 24 666.0 20.20 109.85 23.27 13.40 437 | 14.42080 0.00 18.100 0 0.7400 6.4610 93.30 2.0026 24 666.0 20.20 27.49 18.05 9.60 438 | 15.17720 0.00 18.100 0 0.7400 6.1520 100.00 1.9142 24 666.0 20.20 9.32 26.45 8.70 439 | 13.67810 0.00 18.100 0 0.7400 5.9350 87.90 1.8206 24 666.0 20.20 68.95 34.02 8.40 440 | 9.39063 0.00 18.100 0 0.7400 5.6270 93.90 1.8172 24 666.0 20.20 396.90 22.88 12.80 441 | 22.05110 0.00 18.100 0 0.7400 5.8180 92.40 1.8662 24 666.0 20.20 391.45 22.11 10.50 442 | 9.72418 0.00 18.100 0 0.7400 6.4060 97.20 2.0651 24 666.0 20.20 385.96 19.52 17.10 443 | 5.66637 0.00 18.100 0 0.7400 6.2190 100.00 2.0048 24 666.0 20.20 395.69 16.59 18.40 444 | 9.96654 0.00 18.100 0 0.7400 6.4850 100.00 1.9784 24 666.0 20.20 386.73 18.85 15.40 445 | 12.80230 0.00 18.100 0 0.7400 5.8540 96.60 1.8956 24 666.0 20.20 240.52 23.79 10.80 446 | 10.67180 0.00 18.100 0 0.7400 6.4590 94.80 1.9879 24 666.0 20.20 43.06 23.98 11.80 447 | 6.28807 0.00 18.100 0 0.7400 6.3410 96.40 2.0720 24 666.0 20.20 318.01 17.79 14.90 448 | 9.92485 0.00 18.100 0 0.7400 6.2510 96.60 2.1980 24 666.0 20.20 388.52 16.44 12.60 449 | 9.32909 0.00 18.100 0 0.7130 6.1850 98.70 2.2616 24 666.0 20.20 396.90 18.13 14.10 450 | 7.52601 0.00 18.100 0 0.7130 6.4170 98.30 2.1850 24 666.0 20.20 304.21 19.31 13.00 451 | 6.71772 0.00 18.100 0 0.7130 6.7490 92.60 2.3236 24 666.0 20.20 0.32 17.44 13.40 452 | 5.44114 0.00 18.100 0 0.7130 6.6550 98.20 2.3552 24 666.0 20.20 355.29 17.73 15.20 453 | 5.09017 0.00 18.100 0 0.7130 6.2970 91.80 2.3682 24 666.0 20.20 385.09 17.27 16.10 454 | 8.24809 0.00 18.100 0 0.7130 7.3930 99.30 2.4527 24 666.0 20.20 375.87 16.74 17.80 455 | 9.51363 0.00 18.100 0 0.7130 6.7280 94.10 2.4961 24 666.0 20.20 6.68 18.71 14.90 456 | 4.75237 0.00 18.100 0 0.7130 6.5250 86.50 2.4358 24 666.0 20.20 50.92 18.13 14.10 457 | 4.66883 0.00 18.100 0 0.7130 5.9760 87.90 2.5806 24 666.0 20.20 10.48 19.01 12.70 458 | 8.20058 0.00 18.100 0 0.7130 5.9360 80.30 2.7792 24 666.0 20.20 3.50 16.94 13.50 459 | 7.75223 0.00 18.100 0 0.7130 6.3010 83.70 2.7831 24 666.0 20.20 272.21 16.23 14.90 460 | 6.80117 0.00 18.100 0 0.7130 6.0810 84.40 2.7175 24 666.0 20.20 396.90 14.70 20.00 461 | 4.81213 0.00 18.100 0 0.7130 6.7010 90.00 2.5975 24 666.0 20.20 255.23 16.42 16.40 462 | 3.69311 0.00 18.100 0 0.7130 6.3760 88.40 2.5671 24 666.0 20.20 391.43 14.65 17.70 463 | 6.65492 0.00 18.100 0 0.7130 6.3170 83.00 2.7344 24 666.0 20.20 396.90 13.99 19.50 464 | 5.82115 0.00 18.100 0 0.7130 6.5130 89.90 2.8016 24 666.0 20.20 393.82 10.29 20.20 465 | 7.83932 0.00 18.100 0 0.6550 6.2090 65.40 2.9634 24 666.0 20.20 396.90 13.22 21.40 466 | 3.16360 0.00 18.100 0 0.6550 5.7590 48.20 3.0665 24 666.0 20.20 334.40 14.13 19.90 467 | 3.77498 0.00 18.100 0 0.6550 5.9520 84.70 2.8715 24 666.0 20.20 22.01 17.15 19.00 468 | 4.42228 0.00 18.100 0 0.5840 6.0030 94.50 2.5403 24 666.0 20.20 331.29 21.32 19.10 469 | 15.57570 0.00 18.100 0 0.5800 5.9260 71.00 2.9084 24 666.0 20.20 368.74 18.13 19.10 470 | 13.07510 0.00 18.100 0 0.5800 5.7130 56.70 2.8237 24 666.0 20.20 396.90 14.76 20.10 471 | 4.34879 0.00 18.100 0 0.5800 6.1670 84.00 3.0334 24 666.0 20.20 396.90 16.29 19.90 472 | 4.03841 0.00 18.100 0 0.5320 6.2290 90.70 3.0993 24 666.0 20.20 395.33 12.87 19.60 473 | 3.56868 0.00 18.100 0 0.5800 6.4370 75.00 2.8965 24 666.0 20.20 393.37 14.36 23.20 474 | 4.64689 0.00 18.100 0 0.6140 6.9800 67.60 2.5329 24 666.0 20.20 374.68 11.66 29.80 475 | 8.05579 0.00 18.100 0 0.5840 5.4270 95.40 2.4298 24 666.0 20.20 352.58 18.14 13.80 476 | 6.39312 0.00 18.100 0 0.5840 6.1620 97.40 2.2060 24 666.0 20.20 302.76 24.10 13.30 477 | 4.87141 0.00 18.100 0 0.6140 6.4840 93.60 2.3053 24 666.0 20.20 396.21 18.68 16.70 478 | 15.02340 0.00 18.100 0 0.6140 5.3040 97.30 2.1007 24 666.0 20.20 349.48 24.91 12.00 479 | 10.23300 0.00 18.100 0 0.6140 6.1850 96.70 2.1705 24 666.0 20.20 379.70 18.03 14.60 480 | 14.33370 0.00 18.100 0 0.6140 6.2290 88.00 1.9512 24 666.0 20.20 383.32 13.11 21.40 481 | 5.82401 0.00 18.100 0 0.5320 6.2420 64.70 3.4242 24 666.0 20.20 396.90 10.74 23.00 482 | 5.70818 0.00 18.100 0 0.5320 6.7500 74.90 3.3317 24 666.0 20.20 393.07 7.74 23.70 483 | 5.73116 0.00 18.100 0 0.5320 7.0610 77.00 3.4106 24 666.0 20.20 395.28 7.01 25.00 484 | 2.81838 0.00 18.100 0 0.5320 5.7620 40.30 4.0983 24 666.0 20.20 392.92 10.42 21.80 485 | 2.37857 0.00 18.100 0 0.5830 5.8710 41.90 3.7240 24 666.0 20.20 370.73 13.34 20.60 486 | 3.67367 0.00 18.100 0 0.5830 6.3120 51.90 3.9917 24 666.0 20.20 388.62 10.58 21.20 487 | 5.69175 0.00 18.100 0 0.5830 6.1140 79.80 3.5459 24 666.0 20.20 392.68 14.98 19.10 488 | 4.83567 0.00 18.100 0 0.5830 5.9050 53.20 3.1523 24 666.0 20.20 388.22 11.45 20.60 489 | 0.15086 0.00 27.740 0 0.6090 5.4540 92.70 1.8209 4 711.0 20.10 395.09 18.06 15.20 490 | 0.18337 0.00 27.740 0 0.6090 5.4140 98.30 1.7554 4 711.0 20.10 344.05 23.97 7.00 491 | 0.20746 0.00 27.740 0 0.6090 5.0930 98.00 1.8226 4 711.0 20.10 318.43 29.68 8.10 492 | 0.10574 0.00 27.740 0 0.6090 5.9830 98.80 1.8681 4 711.0 20.10 390.11 18.07 13.60 493 | 0.11132 0.00 27.740 0 0.6090 5.9830 83.50 2.1099 4 711.0 20.10 396.90 13.35 20.10 494 | 0.17331 0.00 9.690 0 0.5850 5.7070 54.00 2.3817 6 391.0 19.20 396.90 12.01 21.80 495 | 0.27957 0.00 9.690 0 0.5850 5.9260 42.60 2.3817 6 391.0 19.20 396.90 13.59 24.50 496 | 0.17899 0.00 9.690 0 0.5850 5.6700 28.80 2.7986 6 391.0 19.20 393.29 17.60 23.10 497 | 0.28960 0.00 9.690 0 0.5850 5.3900 72.90 2.7986 6 391.0 19.20 396.90 21.14 19.70 498 | 0.26838 0.00 9.690 0 0.5850 5.7940 70.60 2.8927 6 391.0 19.20 396.90 14.10 18.30 499 | 0.23912 0.00 9.690 0 0.5850 6.0190 65.30 2.4091 6 391.0 19.20 396.90 12.92 21.20 500 | 0.17783 0.00 9.690 0 0.5850 5.5690 73.50 2.3999 6 391.0 19.20 395.77 15.10 17.50 501 | 0.22438 0.00 9.690 0 0.5850 6.0270 79.70 2.4982 6 391.0 19.20 396.90 14.33 16.80 502 | 0.06263 0.00 11.930 0 0.5730 6.5930 69.10 2.4786 1 273.0 21.00 391.99 9.67 22.40 503 | 0.04527 0.00 11.930 0 0.5730 6.1200 76.70 2.2875 1 273.0 21.00 396.90 9.08 20.60 504 | 0.06076 0.00 11.930 0 0.5730 6.9760 91.00 2.1675 1 273.0 21.00 396.90 5.64 23.90 505 | 0.10959 0.00 11.930 0 0.5730 6.7940 89.30 2.3889 1 273.0 21.00 393.45 6.48 22.00 506 | 0.04741 0.00 11.930 0 0.5730 6.0300 80.80 2.5050 1 273.0 21.00 396.90 7.88 11.90 507 | 508 | --------------------------------------------------------------------------------