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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Sat May 11 08:56:41 2019
@author: nolte
D. D. Nolte, Introduction to Modern Dynamics: Chaos, Networks, Space and Time, 2nd ed. (Oxford,2019)
"""
# https://www.python-course.eu/networkx.php
# https://networkx.github.io/documentation/stable/tutorial.html
# https://networkx.github.io/documentation/stable/reference/functions.html
import numpy as np
from scipy import integrate
from matplotlib import pyplot as plt
import networkx as nx
from UserFunction import linfit
import time
tstart = time.time()
plt.close('all')
Nfac = 25 # 25
N = 100 # 50
width = 0.2
# model_case 1 = Complete Graph
# model_case 2 = Barabasi
# model_case 3 = Power Law
# model_case 4 = D-dimensional Hypercube
# model_case 5 = Erdos Renyi
# model_case 6 = Random Regular
# model_case 7 = Strogatz
# model_case 8 = Hexagonal lattice
# model_case 9 = Tree
# model_case 10 == 2D square lattice
model_case = int(input('Input Model Case (1-10)'))
if model_case == 1: # Complete Graph
facoef = 0.2
nodecouple = nx.complete_graph(N)
elif model_case == 2: # Barabasi
facoef = 2
k = 3
nodecouple = nx.barabasi_albert_graph(N, k, seed=None)
elif model_case == 3: # Power law
facoef = 3
k = 3
triangle_prob = 0.3
nodecouple = nx.powerlaw_cluster_graph(N, k, triangle_prob)
elif model_case == 4:
Dim = 6
facoef = 3
nodecouple = nx.hypercube_graph(Dim)
N = nodecouple.number_of_nodes()
elif model_case == 5: # Erdos-Renyi
facoef = 5
prob = 0.1
nodecouple = nx.erdos_renyi_graph(N, prob, seed=None, directed=False)
elif model_case == 6: # Random
facoef = 5
nodecouple = nx.random_regular_graph(3, N, seed=None)
elif model_case == 7: # Watts
facoef = 7
k = 4; # nearest neighbors
rewire_prob = 0.2 # rewiring probability
nodecouple = nx.watts_strogatz_graph(N, k, rewire_prob, seed=None)
elif model_case == 8:
facoef = 8
rows = 4
colm = 8
nodecouple = nx.hexagonal_lattice_graph(rows, colm, periodic=True, with_positions=False)
N = nodecouple.number_of_nodes()
elif model_case == 9: # k-fold tree
facoef = 16
k = 3 # degree
h = 3 # height
sm = 0
for lp in range(h+1):
sm = sm + k**lp
N = sm
nodecouple = nx.balanced_tree(k, h)
elif model_case == 10: # square lattice
facoef = 3
m = 6
n = 6
nodecouple = nx.grid_2d_graph(m, n, periodic=True)
N = nodecouple.number_of_nodes()
plt.figure(1)
nx.draw(nodecouple)
#nx.draw_circular(nodecouple)
#nx.draw_spring(nodecouple)
#nx.draw_spectral(nodecouple)
print('Number of nodes = ',nodecouple.number_of_nodes())
print('Number of edges = ',nodecouple.number_of_edges())
#print('Average degree = ',nx.k_nearest_neighbors(nodecouple))
# function: omegout, yout = coupleN(G)
def coupleN(G):
# function: yd = flow_deriv(x_y)
def flow_deriv(y,t0):
yp = np.zeros(shape=(N,))
ind = -1
for omloop in G.node:
ind = ind + 1
temp = omega[ind]
linksz = G.node[omloop]['numlink']
for cloop in range(linksz):
cindex = G.node[omloop]['link'][cloop]
indx = G.node[cindex]['index']
g = G.node[omloop]['coupling'][cloop]
temp = temp + g*np.sin(y[indx]-y[ind])
yp[ind] = temp
yd = np.zeros(shape=(N,))
for omloop in range(N):
yd[omloop] = yp[omloop]
return yd
# end of function flow_deriv(x_y)
mnomega = 1.0
ind = -1
for nodeloop in G.node:
ind = ind + 1
omega[ind] = G.node[nodeloop]['element']
x_y_z = omega
# Settle-down Solve for the trajectories
tsettle = 100
t = np.linspace(0, tsettle, tsettle)
x_t = integrate.odeint(flow_deriv, x_y_z, t)
x0 = x_t[tsettle-1,0:N]
t = np.linspace(0,1000,1000)
y = integrate.odeint(flow_deriv, x0, t)
siztmp = np.shape(y)
sy = siztmp[0]
# Fit the frequency
m = np.zeros(shape = (N,))
w = np.zeros(shape = (N,))
mtmp = np.zeros(shape=(4,))
btmp = np.zeros(shape=(4,))
for omloop in range(N):
if np.remainder(sy,4) == 0:
mtmp[0],btmp[0] = linfit(t[0:sy//2],y[0:sy//2,omloop]);
mtmp[1],btmp[1] = linfit(t[sy//2+1:sy],y[sy//2+1:sy,omloop]);
mtmp[2],btmp[2] = linfit(t[sy//4+1:3*sy//4],y[sy//4+1:3*sy//4,omloop]);
mtmp[3],btmp[3] = linfit(t,y[:,omloop]);
else:
sytmp = 4*np.floor(sy/4);
mtmp[0],btmp[0] = linfit(t[0:sytmp//2],y[0:sytmp//2,omloop]);
mtmp[1],btmp[1] = linfit(t[sytmp//2+1:sytmp],y[sytmp//2+1:sytmp,omloop]);
mtmp[2],btmp[2] = linfit(t[sytmp//4+1:3*sytmp/4],y[sytmp//4+1:3*sytmp//4,omloop]);
mtmp[3],btmp[3] = linfit(t[0:sytmp],y[0:sytmp,omloop]);
#m[omloop] = np.median(mtmp)
m[omloop] = np.mean(mtmp)
w[omloop] = mnomega + m[omloop]
omegout = m
yout = y
return omegout, yout
# end of function: omegout, yout = coupleN(G)
Nlink = N*(N-1)//2
omega = np.zeros(shape=(N,))
omegatemp = width*(np.random.rand(N)-1)
meanomega = np.mean(omegatemp)
omega = omegatemp - meanomega
sto = np.std(omega)
lnk = np.zeros(shape = (N,), dtype=int)
ind = -1
for loop in nodecouple.node:
ind = ind + 1
nodecouple.node[loop]['index'] = ind
nodecouple.node[loop]['element'] = omega[ind]
nodecouple.node[loop]['link'] = list(nx.neighbors(nodecouple,loop))
nodecouple.node[loop]['numlink'] = len(list(nx.neighbors(nodecouple,loop)))
lnk[ind] = len(list(nx.neighbors(nodecouple,loop)))
avgdegree = np.mean(lnk)
mnomega = 1
facval = np.zeros(shape = (Nfac,))
yy = np.zeros(shape=(Nfac,N))
xx = np.zeros(shape=(Nfac,))
for facloop in range(Nfac):
print(facloop)
fac = facoef*(16*facloop/(Nfac))*(1/(N-1))*sto/mnomega
ind = -1
for nodeloop in nodecouple.node:
ind = ind + 1
nodecouple.node[nodeloop]['coupling'] = np.zeros(shape=(lnk[ind],))
for linkloop in range (lnk[ind]):
nodecouple.node[nodeloop]['coupling'][linkloop] = fac
facval[facloop] = fac*avgdegree
omegout, yout = coupleN(nodecouple) # Here is the subfunction call for the flow
for omloop in range(N):
yy[facloop,omloop] = omegout[omloop]
xx[facloop] = facval[facloop]
plt.figure(2)
lines = plt.plot(xx,yy)
plt.setp(lines, linewidth=0.5)
plt.show()
elapsed_time = time.time() - tstart
print('elapsed time = ',format(elapsed_time,'.2f'),'secs')
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