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Jan 29, 2021
Jan 29, 2021
Jan 29, 2021
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#!/usr/bin/env python3
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# -*- coding: utf-8 -*-
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"""
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Created on Sat May 11 08:56:41 2019
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@author: nolte
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D. D. Nolte, Introduction to Modern Dynamics: Chaos, Networks, Space and Time, 2nd ed. (Oxford,2019)
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"""
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# https://www.python-course.eu/networkx.php
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# https://networkx.github.io/documentation/stable/tutorial.html
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# https://networkx.github.io/documentation/stable/reference/functions.html
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import numpy as np
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from scipy import integrate
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from matplotlib import pyplot as plt
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import networkx as nx
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from UserFunction import linfit
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import time
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tstart = time.time()
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plt.close('all')
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Nfac = 25 # 25
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width = 0.2
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# model_case 1 = Complete Graph
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# model_case 2 = Barabasi
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# model_case 3 = Power Law
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# model_case 4 = D-dimensional Hypercube
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# model_case 5 = Erdos Renyi
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# model_case 6 = Random Regular
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# model_case 7 = Strogatz
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# model_case 8 = Hexagonal lattice
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# model_case 9 = Tree
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# model_case 10 == 2D square lattice
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model_case = int(input('Input Model Case (1-10)'))
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if model_case == 1: # Complete Graph
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facoef = 0.2
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nodecouple = nx.complete_graph(N)
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elif model_case == 2: # Barabasi
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facoef = 2
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k = 3
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nodecouple = nx.barabasi_albert_graph(N, k, seed=None)
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elif model_case == 3: # Power law
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facoef = 3
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k = 3
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triangle_prob = 0.3
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nodecouple = nx.powerlaw_cluster_graph(N, k, triangle_prob)
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elif model_case == 4:
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Dim = 6
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facoef = 3
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nodecouple = nx.hypercube_graph(Dim)
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N = nodecouple.number_of_nodes()
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elif model_case == 5: # Erdos-Renyi
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facoef = 5
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prob = 0.1
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nodecouple = nx.erdos_renyi_graph(N, prob, seed=None, directed=False)
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elif model_case == 6: # Random
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facoef = 5
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nodecouple = nx.random_regular_graph(3, N, seed=None)
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elif model_case == 7: # Watts
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facoef = 7
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k = 4; # nearest neighbors
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rewire_prob = 0.2 # rewiring probability
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nodecouple = nx.watts_strogatz_graph(N, k, rewire_prob, seed=None)
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elif model_case == 8:
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facoef = 8
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rows = 4
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colm = 8
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nodecouple = nx.hexagonal_lattice_graph(rows, colm, periodic=True, with_positions=False)
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N = nodecouple.number_of_nodes()
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elif model_case == 9: # k-fold tree
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facoef = 16
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k = 3 # degree
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h = 3 # height
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sm = 0
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for lp in range(h+1):
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sm = sm + k**lp
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N = sm
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nodecouple = nx.balanced_tree(k, h)
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elif model_case == 10: # square lattice
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facoef = 3
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m = 6
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n = 6
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N = nodecouple.number_of_nodes()
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plt.figure(1)
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nx.draw(nodecouple)
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#nx.draw_circular(nodecouple)
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#nx.draw_spring(nodecouple)
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#nx.draw_spectral(nodecouple)
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print('Number of nodes = ',nodecouple.number_of_nodes())
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print('Number of edges = ',nodecouple.number_of_edges())
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#print('Average degree = ',nx.k_nearest_neighbors(nodecouple))
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# function: omegout, yout = coupleN(G)
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def coupleN(G):
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# function: yd = flow_deriv(x_y)
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def flow_deriv(y,t0):
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yp = np.zeros(shape=(N,))
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ind = -1
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for omloop in G.node:
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ind = ind + 1
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temp = omega[ind]
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linksz = G.node[omloop]['numlink']
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for cloop in range(linksz):
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cindex = G.node[omloop]['link'][cloop]
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indx = G.node[cindex]['index']
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g = G.node[omloop]['coupling'][cloop]
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temp = temp + g*np.sin(y[indx]-y[ind])
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yp[ind] = temp
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yd = np.zeros(shape=(N,))
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for omloop in range(N):
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yd[omloop] = yp[omloop]
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return yd
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# end of function flow_deriv(x_y)
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mnomega = 1.0
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ind = -1
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for nodeloop in G.node:
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ind = ind + 1
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omega[ind] = G.node[nodeloop]['element']
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x_y_z = omega
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# Settle-down Solve for the trajectories
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tsettle = 100
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t = np.linspace(0, tsettle, tsettle)
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x_t = integrate.odeint(flow_deriv, x_y_z, t)
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x0 = x_t[tsettle-1,0:N]
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y = integrate.odeint(flow_deriv, x0, t)
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siztmp = np.shape(y)
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sy = siztmp[0]
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# Fit the frequency
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m = np.zeros(shape = (N,))
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w = np.zeros(shape = (N,))
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mtmp = np.zeros(shape=(4,))
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btmp = np.zeros(shape=(4,))
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for omloop in range(N):
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if np.remainder(sy,4) == 0:
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mtmp[0],btmp[0] = linfit(t[0:sy//2],y[0:sy//2,omloop]);
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mtmp[1],btmp[1] = linfit(t[sy//2+1:sy],y[sy//2+1:sy,omloop]);
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mtmp[2],btmp[2] = linfit(t[sy//4+1:3*sy//4],y[sy//4+1:3*sy//4,omloop]);
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mtmp[3],btmp[3] = linfit(t,y[:,omloop]);
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else:
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sytmp = 4*np.floor(sy/4);
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mtmp[0],btmp[0] = linfit(t[0:sytmp//2],y[0:sytmp//2,omloop]);
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mtmp[1],btmp[1] = linfit(t[sytmp//2+1:sytmp],y[sytmp//2+1:sytmp,omloop]);
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mtmp[2],btmp[2] = linfit(t[sytmp//4+1:3*sytmp/4],y[sytmp//4+1:3*sytmp//4,omloop]);
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mtmp[3],btmp[3] = linfit(t[0:sytmp],y[0:sytmp,omloop]);
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#m[omloop] = np.median(mtmp)
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m[omloop] = np.mean(mtmp)
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w[omloop] = mnomega + m[omloop]
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omegout = m
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yout = y
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return omegout, yout
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# end of function: omegout, yout = coupleN(G)
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Nlink = N*(N-1)//2
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omega = np.zeros(shape=(N,))
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omegatemp = width*(np.random.rand(N)-1)
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meanomega = np.mean(omegatemp)
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omega = omegatemp - meanomega
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sto = np.std(omega)
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lnk = np.zeros(shape = (N,), dtype=int)
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ind = -1
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for loop in nodecouple.node:
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ind = ind + 1
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nodecouple.node[loop]['index'] = ind
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nodecouple.node[loop]['element'] = omega[ind]
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nodecouple.node[loop]['link'] = list(nx.neighbors(nodecouple,loop))
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nodecouple.node[loop]['numlink'] = len(list(nx.neighbors(nodecouple,loop)))
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lnk[ind] = len(list(nx.neighbors(nodecouple,loop)))
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avgdegree = np.mean(lnk)
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mnomega = 1
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facval = np.zeros(shape = (Nfac,))
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yy = np.zeros(shape=(Nfac,N))
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xx = np.zeros(shape=(Nfac,))
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for facloop in range(Nfac):
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print(facloop)
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fac = facoef*(16*facloop/(Nfac))*(1/(N-1))*sto/mnomega
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ind = -1
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for nodeloop in nodecouple.node:
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ind = ind + 1
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nodecouple.node[nodeloop]['coupling'] = np.zeros(shape=(lnk[ind],))
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for linkloop in range (lnk[ind]):
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nodecouple.node[nodeloop]['coupling'][linkloop] = fac
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facval[facloop] = fac*avgdegree
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omegout, yout = coupleN(nodecouple) # Here is the subfunction call for the flow
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for omloop in range(N):
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yy[facloop,omloop] = omegout[omloop]
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xx[facloop] = facval[facloop]
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plt.figure(2)
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lines = plt.plot(xx,yy)
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plt.setp(lines, linewidth=0.5)
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plt.show()
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elapsed_time = time.time() - tstart
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print('elapsed time = ',format(elapsed_time,'.2f'),'secs')