├── README.md ├── convergencyOrderIntegration.ipynb ├── ddeint.py ├── generate_setup.ipynb ├── matplotlib_latex_configurations.py ├── network_of_oscillators_Kuramoto_model.py ├── network_of_oscillators_integrate_and_sync_quantifiers.py ├── network_of_oscillators_plot_utils.py ├── parameters ├── N0011_BA002_001.net ├── N0011_C001.Freq ├── N0011_C002.Freq ├── N0011_ER002_001.Net ├── N0011_R001.Ic └── N0011_U001.Freq ├── run_integrate_measure_and_plot.ipynb └── tex_example ├── Example.aux ├── Example.bbl ├── Example.blg ├── Example.log ├── Example.pdf ├── Example.synctex.gz ├── Example.tex ├── Macros.sty ├── References.bib ├── graph.pdf ├── orderParameter080.pdf ├── orderParameter095.pdf ├── phaseVariables080.pdf └── phaseVariables095.pdf /README.md: -------------------------------------------------------------------------------- 1 | # kuramoto_model_integrate_and_plot 2 | 3 | Check run_integrate_measure_and_plot.ipynb! 4 | 5 | This repository provides Python code to perform numerical integration of the Kuramoto Model, a network of coupled non-identical phase oscillators. It allows simulations via odeint from scipy.integrate (ODEs) or ddeint (DDEs), in the presence of overall communication delay between oscillators. 6 | 7 | We also configure and present suggestions for figures which are suitable for Latex (see tex_example/Example.pdf). 8 | 9 | The Kuramoto vector field is defined in network_of_oscillators_Kuramoto_model.py and its parameters are loaded from the /parameters folder. 10 | 11 | We require several packages (numpy, scipy, matplotlib, etc). The standard installation of https://anaconda.org/anaconda/python contains all of them. 12 | 13 | TODO: unit tests, complete documentation. 14 | 15 | 16 | -------------------------------------------------------------------------------- /convergencyOrderIntegration.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "code", 5 | "execution_count": 101, 6 | "metadata": { 7 | "collapsed": true 8 | }, 9 | "outputs": [], 10 | "source": [ 11 | "import numpy as np\n", 12 | "from scipy.integrate import odeint\n", 13 | "from ddeint import ddeint\n", 14 | "import matplotlib.pyplot as plt" 15 | ] 16 | }, 17 | { 18 | "cell_type": "markdown", 19 | "metadata": { 20 | "collapsed": true 21 | }, 22 | "source": [ 23 | "This notebook computes the convergency order (p) of odeint and ddeint according to \n", 24 | "[Richard L. Burden, J. Douglas Faires, Numerical Analysis, 2010]" 25 | ] 26 | }, 27 | { 28 | "cell_type": "markdown", 29 | "metadata": { 30 | "collapsed": true 31 | }, 32 | "source": [ 33 | "odeint is tested against x'(t) = x" 34 | ] 35 | }, 36 | { 37 | "cell_type": "code", 38 | "execution_count": 102, 39 | "metadata": {}, 40 | "outputs": [], 41 | "source": [ 42 | "def f1(x, t):\n", 43 | " return x\n", 44 | "\n", 45 | "x0 = 1\n", 46 | "tf = 10\n", 47 | "sol_ref = np.exp(tf)" 48 | ] 49 | }, 50 | { 51 | "cell_type": "code", 52 | "execution_count": 103, 53 | "metadata": {}, 54 | "outputs": [ 55 | { 56 | "name": "stdout", 57 | "output_type": "stream", 58 | "text": [ 59 | "h= 1.00e-01 , error= 3.35e-04\n", 60 | "h= 5.00e-02 , error= 2.04e-04 , p= 7.21e-01\n", 61 | "h= 2.50e-02 , error= 2.31e-04 , p=-1.80e-01\n", 62 | "h= 1.25e-02 , error= 6.74e-05 , p= 1.78e+00\n", 63 | "h= 6.25e-03 , error= 5.24e-04 , p=-2.96e+00\n", 64 | "h= 3.13e-03 , error= 1.40e-04 , p= 1.90e+00\n", 65 | "h= 1.56e-03 , error= 1.75e-05 , p= 3.00e+00\n", 66 | "h= 7.81e-04 , error= 2.20e-06 , p= 2.99e+00\n" 67 | ] 68 | } 69 | ], 70 | "source": [ 71 | "h = 0.1\n", 72 | "for i in range(8):\n", 73 | " t = np.arange(0, tf + h / 2, h)\n", 74 | " x = odeint(f1, x0, t, hmax= h)\n", 75 | " if i == 0:\n", 76 | " auxErr1 = abs( x[-1][0] - sol_ref)\n", 77 | " print(\"h=%9.2e\"% (h), \", error=%9.2e\"% (auxErr1))\n", 78 | " else:\n", 79 | " auxErr2 = abs( x[-1][0] - sol_ref)\n", 80 | " p = np.log(auxErr1 / auxErr2) / np.log(2.0)\n", 81 | " print(\"h=%9.2e\"% (h), \", error=%9.2e\"% (auxErr2), \", p=%9.2e\"% (p))\n", 82 | " auxErr1 = auxErr2\n", 83 | " h = h / 2" 84 | ] 85 | }, 86 | { 87 | "cell_type": "markdown", 88 | "metadata": { 89 | "collapsed": true 90 | }, 91 | "source": [ 92 | "ddeint is tested against x'(t) = x(t- pi/2)" 93 | ] 94 | }, 95 | { 96 | "cell_type": "code", 97 | "execution_count": 104, 98 | "metadata": { 99 | "collapsed": true 100 | }, 101 | "outputs": [], 102 | "source": [ 103 | "def f2(x, t):\n", 104 | " return -x(t - np.pi / 2)\n", 105 | "hist = lambda t: np.sin(t)" 106 | ] 107 | }, 108 | { 109 | "cell_type": "code", 110 | "execution_count": 108, 111 | "metadata": {}, 112 | "outputs": [], 113 | "source": [ 114 | "h = np.pi / 2\n", 115 | "sol_ref = np.sin(tf)\n", 116 | "tf = 10.0 * h" 117 | ] 118 | }, 119 | { 120 | "cell_type": "code", 121 | "execution_count": 109, 122 | "metadata": {}, 123 | "outputs": [ 124 | { 125 | "name": "stdout", 126 | "output_type": "stream", 127 | "text": [ 128 | "h= 1.57e+00 , error= 3.18e-01\n", 129 | "h= 7.85e-01 , error= 1.85e-01 , p= 7.85e-01\n", 130 | "h= 3.93e-01 , error= 5.59e-02 , p= 1.73e+00\n", 131 | "h= 1.96e-01 , error= 1.47e-02 , p= 1.93e+00\n", 132 | "h= 9.82e-02 , error= 3.68e-03 , p= 1.99e+00\n", 133 | "h= 4.91e-02 , error= 9.46e-04 , p= 1.96e+00\n", 134 | "h= 2.45e-02 , error= 2.11e-04 , p= 2.17e+00\n", 135 | "h= 1.23e-02 , error= 4.78e-05 , p= 2.14e+00\n" 136 | ] 137 | } 138 | ], 139 | "source": [ 140 | "for i in range(8):\n", 141 | " t = np.arange(0, tf + h / 2, h)\n", 142 | " x = ddeint(f2, hist, t)\n", 143 | " if i == 0:\n", 144 | " auxErr1 = abs( x[-1] - sol_ref)\n", 145 | " print(\"h=%9.2e\"% (h), \", error=%9.2e\"% (auxErr1))\n", 146 | " else:\n", 147 | " auxErr2 = abs( x[-1] - sol_ref)\n", 148 | " p = np.log(auxErr1 / auxErr2) / np.log(2.0)\n", 149 | " print(\"h=%9.2e\"% (h), \", error=%9.2e\"% (auxErr2), \", p=%9.2e\"% (p))\n", 150 | " auxErr1 = auxErr2\n", 151 | " h = h / 2\n", 152 | " " 153 | ] 154 | }, 155 | { 156 | "cell_type": "code", 157 | "execution_count": null, 158 | "metadata": { 159 | "collapsed": true 160 | }, 161 | "outputs": [], 162 | "source": [] 163 | }, 164 | { 165 | "cell_type": "code", 166 | "execution_count": null, 167 | "metadata": { 168 | "collapsed": true 169 | }, 170 | "outputs": [], 171 | "source": [] 172 | } 173 | ], 174 | "metadata": { 175 | "kernelspec": { 176 | "display_name": "Python 3", 177 | "language": "python", 178 | "name": "python3" 179 | }, 180 | "language_info": { 181 | "codemirror_mode": { 182 | "name": "ipython", 183 | "version": 3 184 | }, 185 | "file_extension": ".py", 186 | "mimetype": "text/x-python", 187 | "name": "python", 188 | "nbconvert_exporter": "python", 189 | "pygments_lexer": "ipython3", 190 | "version": "3.6.1" 191 | } 192 | }, 193 | "nbformat": 4, 194 | "nbformat_minor": 2 195 | } 196 | -------------------------------------------------------------------------------- /ddeint.py: -------------------------------------------------------------------------------- 1 | # Copied from http://codegist.net/snippet/python/ddeintpy_julianeagu_python 2 | # Obs: This DDE integrator uses linear interpolation. 3 | # I still need to determine the convergency order of this method... 4 | 5 | # REQUIRES PACKAGES Numpy AND Scipy INSTALLED 6 | import numpy as np 7 | import scipy.integrate 8 | import scipy.interpolate 9 | 10 | class ddeVar: 11 | """ special function-like variables for the integration of DDEs """ 12 | 13 | def __init__(self,g,tc=0): 14 | """ g(t) = expression of Y(t) for t 0: 77 | dx/dt = 0.5* ( 1- y(t-d) ) 78 | dy/dt = -0.5* ( 1- x(t-d) ) 79 | 80 | Note that here the delay ``d`` is a tunable parameter of the model. 81 | 82 | --- 83 | 84 | import numpy as np 85 | 86 | def model(XY,t,d): 87 | x, y = XY(t) 88 | xd, yd = XY(t-d) 89 | return np.array([0.5*x*(1-yd), -0.5*y*(1-xd)]) 90 | 91 | g = lambda t : np.array([1+t,2-t]) # 'history' at t<0 92 | tt = np.linspace(0,30,20000) # times for integration 93 | d = 0.5 # set parameter d 94 | yy = ddeint(model,g,tt,fargs=(d,)) # solve the DDE ! 95 | 96 | """ 97 | 98 | dde_ = dde(func) 99 | dde_.set_initial_value(ddeVar(g,tt[0])) 100 | dde_.set_f_params(fargs if fargs else []) 101 | return np.array([g(tt[0])]+[dde_.integrate(dde_.t + dt) 102 | for dt in np.diff(tt)]) -------------------------------------------------------------------------------- /generate_setup.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "code", 5 | "execution_count": 15, 6 | "metadata": { 7 | "collapsed": true 8 | }, 9 | "outputs": [], 10 | "source": [ 11 | "%matplotlib inline\n", 12 | "from numpy import *\n", 13 | "from numpy.linalg import *\n", 14 | "from matplotlib.pyplot import *\n", 15 | "import networkx as nx" 16 | ] 17 | }, 18 | { 19 | "cell_type": "code", 20 | "execution_count": null, 21 | "metadata": { 22 | "collapsed": true 23 | }, 24 | "outputs": [], 25 | "source": [] 26 | }, 27 | { 28 | "cell_type": "code", 29 | "execution_count": 16, 30 | "metadata": { 31 | "collapsed": true 32 | }, 33 | "outputs": [], 34 | "source": [ 35 | "\n", 36 | "def write_directed_vertex_list_to_file(g, filename):\n", 37 | " A=array(g.edges())\n", 38 | " A=append(A,A[:,[1,0]], axis=0)\n", 39 | " A=array(A[A[:,0].argsort()]).astype(int)\n", 40 | " savetxt(filename, A, fmt='%i')\n", 41 | "\n", 42 | "\n", 43 | "def unique_rows(a):\n", 44 | " a = ascontiguousarray(a)\n", 45 | " unique_a = unique(a.view([('', a.dtype)]*a.shape[1]))\n", 46 | " return unique_a.view(a.dtype).reshape((unique_a.shape[0], a.shape[1]))\n", 47 | "\n", 48 | "\n", 49 | "def to_undirected_vertex_list(A):\n", 50 | " AA=[[min(A[i]), max(A[i])] for i in range(shape(A)[0])]\n", 51 | " return unique_rows(AA).astype(int).tolist()" 52 | ] 53 | }, 54 | { 55 | "cell_type": "code", 56 | "execution_count": 18, 57 | "metadata": {}, 58 | "outputs": [ 59 | { 60 | "data": { 61 | "image/png": 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81295E+aZCdANwB2INQ+zMvd9B+C7zN/HQeyUEgngHwAt5clX2wNAaGgodenShYL19SlD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\nGjTm7+/Pg8ZUiBeFZywfDx8+xPTp03H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62 | "text/plain": [ 63 | "" 64 | ] 65 | }, 66 | "metadata": {}, 67 | "output_type": "display_data" 68 | } 69 | ], 70 | "source": [ 71 | "g=nx.barabasi_albert_graph(11, 2)\n", 72 | "nx.draw_networkx(g)\n", 73 | "write_directed_vertex_list_to_file(g,'parameters\\\\N0011_BA002_001.net')" 74 | ] 75 | }, 76 | { 77 | "cell_type": "code", 78 | "execution_count": null, 79 | "metadata": { 80 | "collapsed": true 81 | }, 82 | "outputs": [], 83 | "source": [ 84 | "#A=loadtxt('N0010_BA002_001.net')\n", 85 | "#g=nx.Graph(to_undirected_vertex_list(A))\n", 86 | "#nx.draw_networkx(g)" 87 | ] 88 | }, 89 | { 90 | "cell_type": "code", 91 | "execution_count": null, 92 | "metadata": { 93 | "collapsed": true 94 | }, 95 | "outputs": [], 96 | "source": [ 97 | "#w=random.rand(10)\n", 98 | "#savetxt('N0010_U001.Freq', w, fmt='%f')" 99 | ] 100 | }, 101 | { 102 | "cell_type": "code", 103 | "execution_count": null, 104 | "metadata": { 105 | "collapsed": true 106 | }, 107 | "outputs": [], 108 | "source": [ 109 | "#theta0=random.uniform(-pi,pi,10)\n", 110 | "#savetxt('N0010_R001.Ic', theta, fmt='%f')" 111 | ] 112 | }, 113 | { 114 | "cell_type": "code", 115 | "execution_count": 4, 116 | "metadata": { 117 | "collapsed": true 118 | }, 119 | "outputs": [], 120 | "source": [ 121 | "#theta1=random.uniform(-pi,pi,10)\n", 122 | "#savetxt('N0010_R002.Ic', theta1, fmt='%f')" 123 | ] 124 | }, 125 | { 126 | "cell_type": "code", 127 | "execution_count": null, 128 | "metadata": { 129 | "collapsed": true 130 | }, 131 | "outputs": [], 132 | "source": [] 133 | }, 134 | { 135 | "cell_type": "code", 136 | "execution_count": null, 137 | "metadata": { 138 | "collapsed": true 139 | }, 140 | "outputs": [], 141 | "source": [] 142 | }, 143 | { 144 | "cell_type": "code", 145 | "execution_count": 28, 146 | "metadata": { 147 | "collapsed": true 148 | }, 149 | "outputs": [], 150 | "source": [ 151 | "def generate_mean_zero_frequencies(n, a = pi, tol = 0.01):\n", 152 | "\n", 153 | " w = zeros(n)\n", 154 | " w[n-2] = -a\n", 155 | " w[n-1] = a\n", 156 | "\n", 157 | " for i in range(1000):\n", 158 | " w[range(n-2)] = random.uniform(-a,a,n-2)\n", 159 | " if abs(mean(w)) < 0.01:\n", 160 | " return(sort(w))\n", 161 | " break\n", 162 | "\n", 163 | " return nan" 164 | ] 165 | }, 166 | { 167 | "cell_type": "code", 168 | "execution_count": 29, 169 | "metadata": { 170 | "collapsed": true 171 | }, 172 | "outputs": [], 173 | "source": [ 174 | "w = generate_mean_zero_frequencies(10)\n", 175 | "savetxt('parameters/N0010_U001.Freq', w, fmt='%f')" 176 | ] 177 | }, 178 | { 179 | "cell_type": "code", 180 | "execution_count": 31, 181 | "metadata": { 182 | "collapsed": true 183 | }, 184 | "outputs": [], 185 | "source": [] 186 | }, 187 | { 188 | "cell_type": "code", 189 | "execution_count": null, 190 | "metadata": { 191 | "collapsed": true 192 | }, 193 | "outputs": [], 194 | "source": [] 195 | } 196 | ], 197 | "metadata": { 198 | "kernelspec": { 199 | "display_name": "Python 3", 200 | "language": "python", 201 | "name": "python3" 202 | }, 203 | "language_info": { 204 | "codemirror_mode": { 205 | "name": "ipython", 206 | "version": 3 207 | }, 208 | "file_extension": ".py", 209 | "mimetype": "text/x-python", 210 | "name": "python", 211 | "nbconvert_exporter": "python", 212 | "pygments_lexer": "ipython3", 213 | "version": "3.6.1" 214 | } 215 | }, 216 | "nbformat": 4, 217 | "nbformat_minor": 2 218 | } 219 | -------------------------------------------------------------------------------- /matplotlib_latex_configurations.py: -------------------------------------------------------------------------------- 1 | # Configurations to save Matplotlib figures 2 | import matplotlib.pyplot as plt 3 | from pylab import rcParams 4 | 5 | plt.rc('text', usetex=True) 6 | plt.rc('font', family='serif') 7 | 8 | golden_ration = (1 + 5 ** 0.5) / 2 9 | one_column_figure_size = 1.7 10 | rcParams['figure.figsize'] = (one_column_figure_size * golden_ration, one_column_figure_size) 11 | rcParams['axes.linewidth'] = 0.25 12 | rcParams['xtick.major.width'] = 0.25 13 | rcParams['ytick.major.width'] = 0.25 -------------------------------------------------------------------------------- /network_of_oscillators_Kuramoto_model.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | from scipy.integrate import odeint 3 | from ddeint import ddeint 4 | 5 | 6 | class KuramotoModel: 7 | """ Class to hold the Kuramoto Model configuration and perform numerical integration. 8 | 9 | It instantiates a callable object f in such a way that f(theta, t) returns the value of the Kuramoto Model 10 | vector field, where theta is the N-dimensional state variable of the system and t is the time variable. 11 | 12 | Attributes 13 | ---------- 14 | N : int 15 | Quantity of oscillators in the network. 16 | w : ndarray of shape (N) 17 | Natural frequency of each oscillator. 18 | A : list of ndarray of size (N) 19 | Coupling graph as adjacency list, i.e., A[i] contains the neighbor list of the i-th vertex. 20 | d : ndarray of shape (N) 21 | In-degree of the each vertex of the coupling graph. 22 | c : float 23 | Coupling parameter. 24 | tau : float 25 | Overall time delay among nodes. 26 | d_theta : ndarray of shape (N) 27 | Value evaluated of the vector field. 28 | """ 29 | 30 | def __init__(self, w, E, c=1, tau=0): 31 | """ 32 | 33 | Parameters 34 | ---------- 35 | w : ndarray of shape (N) 36 | Natural frequency of each oscillator. 37 | E : ndarray of shape (Ne,2) 38 | Coupling graph as directed edge list of size Ne, i.e, 39 | e[i] = [p, q] means that the p -> q is the i-th directed edge of the coupling graph. 40 | c : float 41 | Coupling parameter. 42 | tau : float 43 | Overall time delay among nodes. 44 | """ 45 | self.N = w.size 46 | self.w = w 47 | self.A = [E[E[:, 0] == i, 1].astype(int) for i in range(0, self.N)] # Edge list E into adjacency list A. 48 | self.d = [len(self.A[i]) for i in range(0, self.N)] 49 | self.c = c 50 | self.d_theta = np.zeros(self.N) 51 | self.tau = tau 52 | 53 | def __call__(self, theta, t=0): 54 | """Evaluate the instance of the Kuramoto Model vector field with the given attributes. 55 | 56 | Parameters 57 | ---------- 58 | theta : ndarray of shape (N) 59 | The phase value of the N oscillators in the network. It must be a function if tau>0. 60 | t: float 61 | The time variable. This parameter allows compatibility with odeint and ddeint from scipy.integrate. 62 | tau: float 63 | Overall time delay among nodes. This parameter is included here to allow compatiblitly with ddeint. 64 | 65 | Returns 66 | ------- 67 | d_theta : ndarray of shape (N) 68 | The evaluated value, that is, d_theta = f(theta, t) 69 | 70 | """ 71 | if self.tau == 0: 72 | theta_t, theta_tau = theta, theta 73 | else: 74 | theta_t, theta_tau = theta(t), theta(t - self.tau) 75 | 76 | for i in range(0, self.N): 77 | self.d_theta[i] = self.w[i] + \ 78 | (self.c / self.d[i]) * sum(np.sin(theta_tau[j] - theta_t[i]) for j in self.A[i]) 79 | 80 | return self.d_theta 81 | 82 | def integrate(self, theta0, tf=100, h=0.01): 83 | """Numerical integation of the Kuramoto Model with odeint (tau=0) or ddeint (tau>0). 84 | 85 | Parameters 86 | ---------- 87 | theta0 : ndarray of shape (N) 88 | Initial condition. If tau>0, (lambda t: theta0 - t * self.w) is used as initial condition. 89 | tf : float 90 | The end of the integration interval. It starts at t=0. 91 | h : float 92 | Numerical integration step. 93 | 94 | Returns 95 | ------- 96 | t : ndarray 97 | Time discretization points, t = [0, h, ..., tf-h, tf]. 98 | theta : ndarray of shape (len(t), N) 99 | Numerical solution for each time in t. 100 | """ 101 | 102 | t = np.arange(0, tf + h / 2, h) 103 | if self.tau == 0: 104 | theta = odeint(self, theta0, t, hmax=h) 105 | else: 106 | theta0_hist = lambda t: theta0 + t * self.w 107 | theta = ddeint(self, theta0_hist, t) 108 | 109 | return t, theta 110 | -------------------------------------------------------------------------------- /network_of_oscillators_integrate_and_sync_quantifiers.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | from scipy.integrate import odeint 3 | 4 | 5 | def arange_(start=0, stop=None, step=1, dtype=None): 6 | """ Alias to np.arange including endpoint. 7 | 8 | Parameters 9 | ---------- 10 | start : number, optional 11 | Start of interval. The default value is 0. 12 | stop : number 13 | End of interval. The interval includes this value. 14 | step : number, optional 15 | Spacing between values. The default vaule is 1. 16 | dtype : dtype 17 | The type of the output array. 18 | 19 | Returns 20 | ------- 21 | arange_ : ndarray 22 | Array of evenly spaced steps from start to stop. 23 | 24 | See Also 25 | -------- 26 | np.arange : Return evenly spaced values within a given interval. 27 | 28 | Examples 29 | -------- 30 | >>> np.arange(3,7) 31 | array([3, 4, 5, 6, 7]) 32 | >>> np.arange(0,1,0.2) 33 | array([0, 0.2, 0.4, 0.6, 0.8, 1]) 34 | """ 35 | return np.arange(start=start, stop=stop+step/2, step=step, dtype=dtype) 36 | 37 | 38 | def order_parameter(theta): 39 | """ Magninute R and angle psi of the complex average of phase oscillators, 40 | where $R \exp \psi = 1/N \Sum_{i=0}^{N-1} \exp \ii \theta_i$. 41 | 42 | Parameters 43 | ---------- 44 | theta : ndarray of shape (N) or (M, N) 45 | Phase variables of N oscilators at a given instant of time 46 | or at M instants of time. 47 | 48 | Returns 49 | ------- 50 | order_parameter : ndarray of shape (2) or (M, 2) 51 | array([R, psi]), at a single instant of time 52 | or [order_parameter(theta[0,:]), ..., order_parameter(theta[M-1,:])] for M instants of time. 53 | 54 | Examples 55 | -------- 56 | >>> #single point in the unit circle yield R = 1. 57 | >>> order_parameter(np.array([0, 2*np.pi, 6*np.pi])) 58 | array([ 1.00000000e+00, -3.26572480e-16]) 59 | 60 | >>> #oscillators uniformly distributed yield R = 0. 61 | >>> order_parameter(np.array([0, np.pi/2, np.pi, 3*np.pi/2])) 62 | array([ 6.20633538e-17, 2.67794504e+00]) 63 | """ 64 | if theta.ndim == 1: 65 | z = sum(np.exp(theta*1j))/len(theta) 66 | return np.array([np.absolute(z), np.angle(z)]) 67 | elif theta.ndim == 2: 68 | return np.array([order_parameter(theta[i]) for i in range(np.shape(theta)[0])]).T 69 | raise Exception('error') 70 | 71 | 72 | def chop(x, p_start=0.0, p_end=1.0): 73 | """ Chops time series by percentages. 74 | 75 | Parameters 76 | ---------- 77 | x : ndarray of shape (T) or (N, T) 78 | Time series of size T or N time series of size T. 79 | p_start : number, optional 80 | Percentage to be chopped at the begining of the time series. 81 | p_end : number, optional 82 | Chop until this percentage. 83 | 84 | Returns 85 | ------- 86 | chop : ndarray of shape (T1) or (N, T1) 87 | Time series chopped. 88 | 89 | Examples 90 | -------- 91 | >>> chop(np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]), 0.1, 0.8) 92 | array([2, 3, 4, 5, 6, 7, 8]) 93 | 94 | """ 95 | if isinstance(x, list): 96 | return [chop(x[i], p_start, p_end) for i in range(len(x))] 97 | elif x.ndim == 1: 98 | return x[max(0, int(len(x) * p_start)) : min(len(x), int(len(x) * p_end))] 99 | raise Exception('error') 100 | 101 | 102 | def partial_sync(theta, psi, h=0.01, s=0.2): 103 | """ Partial Synchronization Index of theta against psi, 104 | """ 105 | if theta.ndim == 2: 106 | return np.array([partial_sync(theta[:,i], psi, h=h, s=s) for i in range(np.shape(theta)[1])]) 107 | elif theta.ndim == 1: 108 | z = sum(h*np.exp((theta[k] - psi[k])*1j) for k in range(int(np.shape(theta)[0]*s), np.shape(theta)[0]-1)) 109 | return np.absolute(z / (h * int(np.shape(theta)[0] * (1 - s))) ) 110 | raise Exception('error') 111 | 112 | 113 | def integrate_and_measure(kuramoto, theta0, tf=300, h=0.01, s=0.2): 114 | #Integrate network and compute some synchronization quantifiers 115 | #s is the percentage of transiente discarded to evalutate these quantifiers. 116 | 117 | t, theta = kuramoto.integrate(theta0, tf=tf, h=h) 118 | r, psi = order_parameter(theta) 119 | 120 | #Evaluate synchronization quantifiers 121 | r_without_transient = chop(r, s) 122 | 123 | min_r = min(r_without_transient) 124 | mean_r = np.mean(r_without_transient) 125 | max_r = max(r_without_transient) 126 | 127 | dot_psi = np.diff(np.unwrap(psi))/h 128 | mean_dot_psi = np.mean(chop(dot_psi, s)) 129 | 130 | s_per_node = partial_sync(theta, psi, h=h, s=s) 131 | mean_s = np.mean(s_per_node) 132 | 133 | info_out = {'t': t, 'theta': theta, 134 | 'r': r, 'psi': psi, 135 | 'dot_psi': dot_psi, 'mean_dot_psi': mean_dot_psi, 136 | 'min_r': min_r, 'mean_r': mean_r, 'max_r': max_r, 137 | 'partial_sync_per_node': s_per_node, 'partial_sync': mean_s} 138 | 139 | return info_out 140 | 141 | 142 | def unpack_print(out): 143 | return out['t'], out['theta'], out['r'], out['psi'] 144 | -------------------------------------------------------------------------------- /network_of_oscillators_plot_utils.py: -------------------------------------------------------------------------------- 1 | import matplotlib.pyplot as plt 2 | import numpy as np 3 | 4 | import networkx as nx 5 | import matplotlib.patheffects as path_effects 6 | from matplotlib.colors import LinearSegmentedColormap 7 | from matplotlib.ticker import MaxNLocator 8 | import matplotlib.patches as patches 9 | from matplotlib.collections import LineCollection 10 | import matplotlib.ticker as ticker 11 | 12 | from network_of_oscillators_integrate_and_sync_quantifiers import * 13 | 14 | 15 | def chop_colormap(cmap, minval=0.0, maxval=1.0, n=100): 16 | new_cmap = LinearSegmentedColormap.from_list( 17 | 'trunc({n},{a:.2f},{b:.2f})'.format(n=cmap.name, a=minval, b=maxval), 18 | cmap(np.linspace(minval, maxval, n))) 19 | return new_cmap 20 | 21 | #This cmap is applied in to node coloring 22 | cmap_aux = LinearSegmentedColormap.from_list("", ["cyan","#580058"]) 23 | 24 | #In gray scale, cyan becomes almost white, this is why we chop the begining of the color map 25 | cyan_purple_cmap = chop_colormap(cmap_aux, 0.05, 1) 26 | 27 | def frequency_to_color(w): 28 | colors_cyan_purple = cyan_purple_cmap(np.linspace(0, 1, 1001)) 29 | w_min = min(w) 30 | w_max = max(w) 31 | return [colors_cyan_purple[int(1000*(w[i] - w_min)/(w_max - w_min))] for i in range(len(w))] 32 | 33 | def plot_coupling_graph(E, w, ax=None): 34 | if ax is None: 35 | ax = plt.gca() 36 | 37 | ax.set_xticks([]) 38 | ax.set_yticks([]) 39 | ax.plot([0, 0], [1,1], linewidth = None) 40 | 41 | G=nx.Graph() 42 | for i in range(len(E)): 43 | G.add_edge(int(E[i,0]), int(E[i,1])) 44 | 45 | pos=nx.kamada_kawai_layout(G) 46 | 47 | nx.draw_networkx(G, 48 | pos = pos, 49 | node_color = frequency_to_color(w), with_labels=False, 50 | node_size=100, 51 | edge_color='gray', ax = ax) 52 | 53 | ax.collections[0].set_edgecolor("black") #Drawing a black border around nodes. 54 | ax.collections[0].set_linewidth(0.5) 55 | 56 | ax.collections[1].set_linewidth(0.5) # Change edges linewidth 57 | 58 | #Creates node labels in white with a black border 59 | for i in range(max(pos)+1): 60 | text = ax.text(pos[i][0], pos[i][1], i, color='white', size = 8, 61 | ha='center', va='center') 62 | text.set_path_effects([path_effects.Stroke(linewidth=1, foreground='black'), 63 | path_effects.Normal()]) 64 | 65 | sm = plt.cm.ScalarMappable(cmap=cyan_purple_cmap, norm=plt.Normalize(vmin=min(w), vmax=max(w))) 66 | sm._A = [] 67 | cb1 = plt.colorbar(sm) 68 | cb1.set_label(r'$\omega_i$') 69 | 70 | return ax 71 | 72 | def mod2pi(y): 73 | maxdif=max(abs(np.diff(y))) 74 | ymod=np.mod(y, 2*np.pi) 75 | pos=np.where(abs(np.diff(ymod)) > maxdif)[0] 76 | ymod[pos]=np.nan 77 | return ymod 78 | 79 | def get_color_from_list(i, color = plt.rcParams['axes.prop_cycle'].by_key()['color']): 80 | if not type(color) is list: color = [color] 81 | return color[np.mod(i, len(color))] 82 | 83 | 84 | def plot_phase_mod_2pi(t, theta, psi = None, tlim = None, 85 | shift_axis = False, 86 | color = plt.rcParams['axes.prop_cycle'].by_key()['color'], 87 | sel = None, 88 | show_right_ax_labels = True, 89 | ax=None): 90 | """ Plot phase variables mod 2pi 91 | 92 | Parameters 93 | ---------- 94 | t : ndarray 95 | Instant of time 96 | theta : ndarray of shape (len(t), N) 97 | Phase variables at each instant of time 98 | psi : ndarray of shape (len(t)) 99 | If provided, plot the difference between phase and psi 100 | tlim : ndarray of shape (2) 101 | Interval of time 102 | shift_axis : boolean 103 | If True, plot each phase on its own axis. 104 | color : 105 | Colors to plot each trajectory 106 | sel : 107 | Select only some oscillators to plot 108 | show_right_ax_labels 109 | ax 110 | 111 | Returns 112 | ------- 113 | 114 | """ 115 | if ax is None: 116 | ax = plt.gca() 117 | 118 | n = np.shape(theta)[1] 119 | 120 | if psi is None: 121 | plot_label_psi = False 122 | psi = np.zeros(len(t)) 123 | else: 124 | plot_label_psi = True 125 | 126 | if tlim is None: 127 | t_indexes = range(len(t)) 128 | else: 129 | t_indexes = np.intersect1d(np.where(t>=tlim[0])[0], np.where(t<=tlim[1])[0]) 130 | 131 | if sel is None: 132 | sel_color = range(n) 133 | sel = range(n) 134 | else: 135 | if color == plt.rcParams['axes.prop_cycle'].by_key()['color']: 136 | sel_color = range(len(sel)) 137 | else: 138 | sel_color = sel 139 | 140 | 141 | shift = 0 142 | if shift_axis: 143 | shift = 1 144 | ax.set_yticks([0, 1]) 145 | ax.yaxis.set_ticklabels([0, 1]) 146 | 147 | ax.plot([t[t_indexes][0], t[t_indexes][-1]],[0,0], color= 'black', linewidth=0.25) 148 | for i in range(len(sel)): 149 | ax.plot([t[t_indexes][0], t[t_indexes][-1]],[i+1,i+1], color= 'black', linewidth=0.25) 150 | 151 | if show_right_ax_labels: 152 | ax2 = ax.twinx() 153 | ax2.plot([t[t_indexes][0], t[t_indexes][-1]], [0, len(sel)], alpha = 0) 154 | ax2.set_ylabel(r'oscilator index: $i$') 155 | 156 | if sel == range(n): 157 | ax2.yaxis.set_major_locator(MaxNLocator(integer=True)) 158 | a=np.array(ax2.get_yticks().tolist()) 159 | a = a[ np.intersect1d(np.where(a>=0)[0], np.where(a< len(sel))[0])] 160 | ax2.set_yticks(a + 0.5) 161 | 162 | a_labels = [int(a[i]) for i in range(len(a))] 163 | ax2.set_yticklabels(a_labels) 164 | else: 165 | a = [ 0.5 + i for i in range(len(sel))] 166 | ax2.set_yticks(a) 167 | 168 | a_labels = [sel[i] for i in range(len(sel))] 169 | ax2.set_yticklabels(a_labels) 170 | else: 171 | ax.plot([0, 1], [0, 1], alpha = 0) 172 | 173 | for i in range(len(sel)): 174 | ax.plot(t[t_indexes], shift * i + mod2pi(theta[t_indexes, sel[i]] - np.unwrap(psi[t_indexes]) - np.pi)/(2*np.pi), 175 | color = get_color_from_list(sel_color[i], color), 176 | linewidth=0.5) 177 | 178 | ax.set_xlabel(r'$t$') 179 | if plot_label_psi: 180 | ax.set_ylabel(r'$(\theta_i - \psi - \pi)/2\pi$') 181 | else: 182 | ax.set_ylabel(r'$(\theta_i - \pi)/2\pi$') 183 | 184 | return ax 185 | 186 | 187 | def generate_array_density_histogram(theta, psi, i, bins=51, discard_transient=0.2): 188 | aux_theta = np.mod(chop(theta[:, i] - psi - np.pi, discard_transient, 1), 2 * np.pi) 189 | results, edges = np.histogram(aux_theta, bins=np.linspace(0, 2 * np.pi, bins), normed=True) 190 | binWidth = edges[1] - edges[0] 191 | 192 | array = results * binWidth 193 | 194 | return array 195 | 196 | 197 | def plot_phase_mod_2pi_histogram(theta, psi=None, bins=51, discard_transient = 0.2, 198 | shift_axis=False, 199 | color=plt.rcParams['axes.prop_cycle'].by_key()['color'], 200 | show_right_ax_labels = True, 201 | sel=None, 202 | ax=None): 203 | """ Similar to plot_phase_mod_2pi, plotting the histogram. 204 | The unit circle is divided into bins and discard_transient controls the percentage of transient 205 | to be discarded at the begining of the time series. 206 | """ 207 | 208 | if ax is None: 209 | ax = plt.gca() 210 | 211 | n = np.shape(theta)[1] 212 | 213 | if psi is None: 214 | plot_label_psi = False 215 | psi = np.zeros(np.shape(theta)[0]) 216 | else: 217 | plot_label_psi = True 218 | 219 | 220 | if sel is None: 221 | sel_color = range(n) 222 | sel = range(n) 223 | else: 224 | if color == plt.rcParams['axes.prop_cycle'].by_key()['color']: 225 | sel_color = range(len(sel)) 226 | else: 227 | sel_color = sel 228 | 229 | shift = 0 230 | if shift_axis: 231 | shift = 1 232 | ax.set_yticks([0, 1]) 233 | ax.yaxis.set_ticklabels([0, 1]) 234 | ax.plot([0, 1], [0, len(sel)], alpha=0) 235 | 236 | if show_right_ax_labels: 237 | ax2 = ax.twinx() 238 | ax2.plot([0, 1], [0, len(sel)], alpha=0) 239 | ax2.set_ylabel(r'oscilator index: $i$') 240 | 241 | if sel == range(n): 242 | ax2.yaxis.set_major_locator(MaxNLocator(integer=True)) 243 | a = np.array(ax2.get_yticks().tolist()) 244 | a = a[np.intersect1d(np.where(a >= 0)[0], np.where(a < len(sel))[0])] 245 | ax2.set_yticks(a + 0.5) 246 | 247 | a_labels = [int(a[i]) for i in range(len(a))] 248 | ax2.set_yticklabels(a_labels) 249 | else: 250 | a = [0.5 + i for i in range(len(sel))] 251 | ax2.set_yticks(a) 252 | 253 | a_labels = [sel[i] for i in range(len(sel))] 254 | ax2.set_yticklabels(a_labels) 255 | else: 256 | ax.plot([0, 1], [0, 1], alpha=0) 257 | 258 | for i in range(len(sel)): 259 | array = generate_array_density_histogram(theta, psi, sel[i], 260 | discard_transient = discard_transient, bins=bins + 1) 261 | 262 | for j in range(bins): 263 | if array[j] > 0: 264 | ax.add_patch(patches.Rectangle( 265 | (j / bins, shift * i), # (x,y) 266 | 1 / bins, # width 267 | max(array[j], 0.01), # height 268 | linewidth=0.25, 269 | alpha=1 if shift_axis else 0.8, 270 | fill=True, 271 | zorder=10, 272 | edgecolor=get_color_from_list(sel_color[i], color) if shift_axis else 'black', 273 | facecolor=get_color_from_list(sel_color[i], color))) 274 | 275 | if shift_axis: 276 | ax.plot([0, 0.03], [0, 0], color='black', linewidth=0.25, zorder=1) 277 | ax.plot([0.97, 1], [0, 0], color='black', linewidth=0.25, zorder=1) 278 | for i in range(len(sel)): 279 | ax.plot([0, 0.03], [i + 1, i + 1], color='black', linewidth=0.25, zorder=1) 280 | ax.plot([0.97, 1], [i + 1, i + 1], color='black', linewidth=0.25, zorder=1) 281 | 282 | ax.set_ylabel(r'density') 283 | if plot_label_psi: 284 | ax.set_xlabel(r'$(\theta_i - \psi - \pi)/2\pi$') 285 | else: 286 | ax.set_xlabel(r'$(\theta_i - \pi)/2\pi$') 287 | 288 | return ax 289 | 290 | 291 | def plot_r_psi(t, r, psi, tlim=None, ax=None): 292 | 293 | if ax is None: 294 | ax = plt.gca() 295 | 296 | if tlim != None: 297 | indexes = np.intersect1d(np.where(t>=tlim[0])[0], np.where(t<=tlim[1])[0]) 298 | else: 299 | indexes = range(len(t)) 300 | 301 | ax.plot(t[indexes], mod2pi(np.unwrap(psi[indexes])) / (2 * np.pi), color='black', linestyle='--', label=r'$\psi$', linewidth=0.5) 302 | ax.plot(t[indexes], r[indexes], color='blue', label=r'$R$', linewidth=0.5) 303 | 304 | ax.set_xlabel(r'$t$') 305 | ax.set_ylabel(r'$\psi/2\pi, R$') 306 | 307 | return ax 308 | 309 | 310 | cmap_density = LinearSegmentedColormap.from_list("", ["orange","#009000","black"]) 311 | 312 | 313 | def plot_r_exp_psi(t, r, psi, tlim=None, ax=None): 314 | if ax is None: 315 | ax = plt.gca() 316 | 317 | if tlim != None: 318 | indexes = np.intersect1d(np.where(t>=tlim[0])[0], np.where(t<=tlim[1])[0]) 319 | else: 320 | indexes = range(len(t)) 321 | 322 | coords = [[r[i] * np.cos(psi[i]), r[i] * np.sin(psi[i])] for i in indexes] 323 | 324 | x, y = zip(*coords) 325 | points = np.array([x, y]).T.reshape(-1, 1, 2) 326 | 327 | segments = np.concatenate([points[:-1], points[1:]], axis=1) 328 | lc = LineCollection(segments, cmap=cmap_density, 329 | norm=plt.Normalize(0, t[indexes[-1]] - t[indexes[0]] )) 330 | lc.set_array(t) 331 | lc.set_linewidth(0.5) 332 | 333 | ax.add_collection(lc) 334 | 335 | ax.set_xlim([-1.1, 1.1]) 336 | ax.set_ylim([-1.1, 1.1]) 337 | 338 | ax.set_xlabel(r'Real($R$ exp $i \psi$)') 339 | ax.set_ylabel(r'Im($R$ exp $i \psi$)') 340 | ax.set_aspect('equal') 341 | 342 | sm = plt.cm.ScalarMappable(cmap=cmap_density, norm=plt.Normalize(vmin=t[indexes[0]], vmax=t[indexes[-1]])) 343 | sm._A = [] 344 | cb1 = plt.colorbar(sm) 345 | cb1.set_label(r't') 346 | 347 | return ax -------------------------------------------------------------------------------- /parameters/N0011_BA002_001.net: -------------------------------------------------------------------------------- 1 | 0 2 2 | 0 3 3 | 0 4 4 | 0 6 5 | 1 2 6 | 1 5 7 | 1 6 8 | 1 7 9 | 2 1 10 | 2 0 11 | 2 10 12 | 2 8 13 | 2 5 14 | 2 4 15 | 2 3 16 | 2 7 17 | 3 0 18 | 3 2 19 | 4 2 20 | 4 0 21 | 5 2 22 | 5 1 23 | 6 1 24 | 6 9 25 | 6 0 26 | 7 2 27 | 7 8 28 | 7 9 29 | 7 1 30 | 8 7 31 | 8 2 32 | 9 6 33 | 9 10 34 | 9 7 35 | 10 2 36 | 10 9 37 | -------------------------------------------------------------------------------- /parameters/N0011_C001.Freq: -------------------------------------------------------------------------------- 1 | 0.5 2 | 0.5 3 | 1.5 4 | 0.5 5 | 1.5 6 | 0.5 7 | 0.5 8 | 0.5 9 | 1.5 10 | 1.5 11 | 0.5 12 | -------------------------------------------------------------------------------- /parameters/N0011_C002.Freq: -------------------------------------------------------------------------------- 1 | 1.5 2 | 0.5 3 | 1.5 4 | 0.5 5 | 0.5 6 | 0.5 7 | 1.5 8 | 0.5 9 | 0.5 10 | 1.5 11 | 0.5 12 | -------------------------------------------------------------------------------- /parameters/N0011_ER002_001.Net: -------------------------------------------------------------------------------- 1 | 0 1 2 | 0 2 3 | 0 3 4 | 0 4 5 | 0 5 6 | 0 6 7 | 0 7 8 | 0 8 9 | 0 9 10 | 0 10 11 | 1 0 12 | 1 2 13 | 1 3 14 | 1 4 15 | 1 5 16 | 1 6 17 | 1 7 18 | 1 8 19 | 1 9 20 | 1 10 21 | 2 0 22 | 2 1 23 | 2 4 24 | 2 5 25 | 2 6 26 | 2 7 27 | 2 8 28 | 2 10 29 | 3 0 30 | 3 1 31 | 3 5 32 | 3 6 33 | 3 7 34 | 3 10 35 | 4 0 36 | 4 1 37 | 4 2 38 | 4 5 39 | 4 6 40 | 4 7 41 | 4 9 42 | 4 10 43 | 5 0 44 | 5 1 45 | 5 2 46 | 5 3 47 | 5 4 48 | 5 6 49 | 5 7 50 | 5 8 51 | 5 9 52 | 5 10 53 | 6 0 54 | 6 1 55 | 6 2 56 | 6 3 57 | 6 4 58 | 6 5 59 | 6 7 60 | 6 8 61 | 6 9 62 | 6 10 63 | 7 0 64 | 7 1 65 | 7 2 66 | 7 3 67 | 7 4 68 | 7 5 69 | 7 6 70 | 7 8 71 | 7 9 72 | 7 10 73 | 8 0 74 | 8 1 75 | 8 2 76 | 8 5 77 | 8 6 78 | 8 7 79 | 8 9 80 | 8 10 81 | 9 0 82 | 9 1 83 | 9 4 84 | 9 5 85 | 9 6 86 | 9 7 87 | 9 8 88 | 9 10 89 | 10 0 90 | 10 1 91 | 10 2 92 | 10 3 93 | 10 4 94 | 10 5 95 | 10 6 96 | 10 7 97 | 10 8 98 | 10 9 99 | -------------------------------------------------------------------------------- /parameters/N0011_R001.Ic: -------------------------------------------------------------------------------- 1 | 0.917137826899 2 | 4.65809429503 3 | 0.94560484505 4 | 4.54832193121 5 | 5.88608189001 6 | 1.14013482687 7 | 3.04921812921 8 | 0.572833366002 9 | 4.53576828641 10 | 6.15318783668 11 | 4.03473894472 12 | -------------------------------------------------------------------------------- /parameters/N0011_U001.Freq: -------------------------------------------------------------------------------- 1 | -3.141593 2 | -2.688248 3 | -2.622932 4 | -2.580255 5 | -1.721075 6 | -0.935027 7 | 2.128966 8 | 2.444749 9 | 2.963254 10 | 3.042909 11 | 3.141593 12 | -------------------------------------------------------------------------------- /tex_example/Example.aux: -------------------------------------------------------------------------------- 1 | \relax 2 | \providecommand\zref@newlabel[2]{} 3 | \providecommand\hyper@newdestlabel[2]{} 4 | \providecommand\AtEndDvi@Check{} 5 | \AtEndDvi@Check 6 | \providecommand\HyperFirstAtBeginDocument{\AtBeginDocument} 7 | \HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined 8 | \global\let\oldcontentsline\contentsline 9 | \gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}} 10 | \global\let\oldnewlabel\newlabel 11 | \gdef\newlabel#1#2{\newlabelxx{#1}#2} 12 | \gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}} 13 | \AtEndDocument{\ifx\hyper@anchor\@undefined 14 | \let\contentsline\oldcontentsline 15 | \let\newlabel\oldnewlabel 16 | \fi} 17 | \fi} 18 | \global\let\hyper@last\relax 19 | \gdef\HyperFirstAtBeginDocument#1{#1} 20 | \providecommand\HyField@AuxAddToFields[1]{} 21 | \providecommand\HyField@AuxAddToCoFields[2]{} 22 | \@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces This is the coupling graph with natural frequencies}}{1}{figure.1}} 23 | \@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Phase variables, coupling parameter $0.8$. Order parameter becomes regular}}{2}{figure.2}} 24 | \@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Phase variables, coupling parameter $0.95$. Phase-locking}}{2}{figure.3}} 25 | \@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces Phase variables, coupling parameter $0.8$}}{4}{figure.4}} 26 | \@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces Phase variables, coupling parameter $0.95$. Phase-locking}}{4}{figure.5}} 27 | \bibstyle{abbrv} 28 | \bibdata{References} 29 | \zref@newlabel{LastPage}{\default{}\page{6}\abspage{6}} 30 | -------------------------------------------------------------------------------- /tex_example/Example.bbl: -------------------------------------------------------------------------------- 1 | \begin{thebibliography}{} 2 | 3 | \end{thebibliography} 4 | -------------------------------------------------------------------------------- /tex_example/Example.blg: -------------------------------------------------------------------------------- 1 | This is BibTeX, Version 0.99dThe top-level auxiliary file: Example.aux 2 | The style file: abbrv.bst 3 | I found no \citation commands---while reading file Example.aux 4 | Database file #1: References.bib 5 | I was expecting a `,' or a `}'---line 43 of file References.bib 6 | : title = A 7 | : Mathematical Model for a Distributed Attack on Targeted Resources in a Computer Network}, 8 | I'm skipping whatever 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https://raw.githubusercontent.com/cbnfreitas/kuramoto_model_integrate_and_plot/9cce7240265cc9846b80ae3e1e1a94fab9ceaf42/tex_example/Example.pdf -------------------------------------------------------------------------------- /tex_example/Example.synctex.gz: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/cbnfreitas/kuramoto_model_integrate_and_plot/9cce7240265cc9846b80ae3e1e1a94fab9ceaf42/tex_example/Example.synctex.gz -------------------------------------------------------------------------------- /tex_example/Example.tex: -------------------------------------------------------------------------------- 1 | \documentclass[twocolumn]{article} 2 | \usepackage{Macros} 3 | 4 | \begin{document} 5 | 6 | \title{...} 7 | \author{} 8 | \maketitle 9 | 10 | \blindtext[2] 11 | 12 | 13 | \begin{figure} 14 | \centering 15 | \includegraphics[scale=1]{graph} 16 | \caption{This is the coupling graph with natural frequencies} 17 | \end{figure} 18 | 19 | \blindtext[2] 20 | 21 | \begin{figure} 22 | \centering 23 | \includegraphics[scale=1]{orderParameter080} 24 | \caption{Phase variables, coupling parameter $0.8$. Order parameter becomes regular} 25 | \end{figure} 26 | 27 | 28 | \begin{figure} 29 | \centering 30 | \includegraphics[scale=1]{orderParameter095} 31 | \caption{Phase variables, coupling parameter $0.95$. Phase-locking} 32 | \end{figure} 33 | 34 | \blindtext[1] 35 | 36 | \newpage 37 | 38 | \blindtext[2] 39 | 40 | \begin{figure*} 41 | \centering 42 | \includegraphics[scale=1]{phaseVariables080} 43 | \caption{Phase variables, coupling parameter $0.8$} 44 | \end{figure*} 45 | 46 | \blindtext[2] 47 | 48 | \begin{figure*} 49 | \centering 50 | \includegraphics[scale=1]{phaseVariables095} 51 | \caption{Phase variables, coupling parameter $0.95$. Phase-locking} 52 | \end{figure*} 53 | 54 | \blindtext[10] 55 | 56 | 57 | \bibliographystyle{abbrv} 58 | \bibliography{References} 59 | 60 | 61 | \end{document} 62 | -------------------------------------------------------------------------------- /tex_example/Macros.sty: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/cbnfreitas/kuramoto_model_integrate_and_plot/9cce7240265cc9846b80ae3e1e1a94fab9ceaf42/tex_example/Macros.sty -------------------------------------------------------------------------------- /tex_example/References.bib: -------------------------------------------------------------------------------- 1 | % Strings 2 | @string{cs = "Complex Systems"} 3 | @string{pl = "Physics Letters"} 4 | @string{prl = "Physical Review Letters"} 5 | @string{pra = "Physical Review A"} 6 | @string{pla = "Physics Letters A"} 7 | @string{pre = "Physical Review E"} 8 | @string{pd = "Physica D"} 9 | @string{jcsc = "Journal of Circuits, Systems and Computers"} 10 | @string{jsv = "Journal of Sound and Vibration"} 11 | @string{ijbc = "International Journal of Bifurcation and Chaos"} 12 | @string{ijc = "International Journal of Control"} 13 | @string{ieeecas = "IEEE Transactions on Circuits and Systems"} 14 | @string{jrssb = "Journal of the Royal Statistical Society B"} 15 | @string{n = "Nature"} 16 | @string{zn = "Z. Naturforsch"} 17 | @string{jfi = "Zeitschrift fuer Naturforschung A"} 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | @article{Muldowney1996, 27 | author = {Li, M. and Muldowney, J.}, 28 | title = {A Geometric Approach to Global-Stability Problems}, 29 | journal = {SIAM Journal on Mathematical Analysis}, 30 | volume = {27}, 31 | number = {4}, 32 | pages = {1070-1083}, 33 | year = {1996}, 34 | doi = {10.1137/S0036141094266449}, 35 | 36 | URL = {http://epubs.siam.org/doi/abs/10.1137/S0036141094266449}, 37 | eprint = {http://epubs.siam.org/doi/pdf/10.1137/S0036141094266449} 38 | } 39 | 40 | 41 | @article{Haldar2013, 42 | author = {Haldar and Mishra1}, 43 | title = A Mathematical Model for a Distributed Attack on Targeted Resources in a Computer Network}, 44 | journal = {Communications in Nonlinear Science and Numerical Simulation}, 45 | volume = {27}, 46 | number = {4}, 47 | pages = {1070-1083}, 48 | year = {2013}, 49 | } 50 | 51 | 52 | 53 | @article{Li1998, 54 | abstract = {{A necessary and sufficient condition for the stability ofn × nmatrices with real entries is proved. Applications to asymptotic stability of equilibria for vector fields are considered. The results offer an alternative to the well-known Routh–Hurwitz conditions.}}, 55 | author = {Li, Michael Y. and Wang, Liancheng}, 56 | citeulike-article-id = {10659845}, 57 | citeulike-linkout-0 = {http://dx.doi.org/10.1006/jmaa.1998.6020}, 58 | doi = {10.1006/jmaa.1998.6020}, 59 | issn = {0022247X}, 60 | journal = {Journal of Mathematical Analysis and Applications}, 61 | keywords = {additive\_compound\_matrix, matrix\_stability, matrix\_stability\_criterion}, 62 | month = sep, 63 | number = {1}, 64 | pages = {249--264}, 65 | posted-at = {2012-05-11 13:13:49}, 66 | priority = {2}, 67 | title = {{A Criterion for Stability of Matrices}}, 68 | url = {http://dx.doi.org/10.1006/jmaa.1998.6020}, 69 | volume = {225}, 70 | year = {1998} 71 | } 72 | 73 | 74 | 75 | @Article{Muldowney1990, 76 | Author = {James S. {Muldowney}}, 77 | Title = {{Compound matrices and ordinary differential equations.}}, 78 | FJournal = {{Rocky Mountain Journal of Mathematics}}, 79 | Journal = {{Rocky Mt. J. Math.}}, 80 | ISSN = {0035-7596}, 81 | Volume = {20}, 82 | Number = {4}, 83 | Pages = {857--872}, 84 | Year = {1990}, 85 | Publisher = {Rocky Mountain Mathematics Consortium, Arizona State University, Tempe, AZ}, 86 | Language = {English}, 87 | DOI = {10.1216/rmjm/1181073047}, 88 | MSC2010 = {34D05 34C25}, 89 | Zbl = {0725.34049} 90 | } 91 | 92 | -------------------------------------------------------------------------------- /tex_example/graph.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/cbnfreitas/kuramoto_model_integrate_and_plot/9cce7240265cc9846b80ae3e1e1a94fab9ceaf42/tex_example/graph.pdf -------------------------------------------------------------------------------- /tex_example/orderParameter080.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/cbnfreitas/kuramoto_model_integrate_and_plot/9cce7240265cc9846b80ae3e1e1a94fab9ceaf42/tex_example/orderParameter080.pdf -------------------------------------------------------------------------------- /tex_example/orderParameter095.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/cbnfreitas/kuramoto_model_integrate_and_plot/9cce7240265cc9846b80ae3e1e1a94fab9ceaf42/tex_example/orderParameter095.pdf -------------------------------------------------------------------------------- /tex_example/phaseVariables080.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/cbnfreitas/kuramoto_model_integrate_and_plot/9cce7240265cc9846b80ae3e1e1a94fab9ceaf42/tex_example/phaseVariables080.pdf -------------------------------------------------------------------------------- /tex_example/phaseVariables095.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/cbnfreitas/kuramoto_model_integrate_and_plot/9cce7240265cc9846b80ae3e1e1a94fab9ceaf42/tex_example/phaseVariables095.pdf --------------------------------------------------------------------------------