Permalink
Cannot retrieve contributors at this time
Name already in use
A tag already exists with the provided branch name. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. Are you sure you want to create this branch?
Python-Programs-for-Nonlinear-Dynamics/SteinsGate2D.py
Go to fileThis commit does not belong to any branch on this repository, and may belong to a fork outside of the repository.
132 lines (107 sloc)
3.04 KB
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
#!/usr/bin/env python3 | |
# -*- coding: utf-8 -*- | |
""" | |
SteinsGate2D.py | |
Created on Sat March 6, 2021 | |
@author: David Nolte | |
Introduction to Modern Dynamics, 2nd edition (Oxford University Press, 2019) | |
2D simulation of Stein's Gate Divergence Meter | |
""" | |
import numpy as np | |
from scipy import integrate | |
from matplotlib import pyplot as plt | |
plt.close('all') | |
def solve_flow(param,lim = [-6,6,-6,6],max_time=20.0): | |
def flow_deriv(x_y, t0, alpha, beta, gamma): | |
#"""Compute the time-derivative .""" | |
x, y = x_y | |
w = 1 | |
R2 = x**2 + y**2 | |
R = np.sqrt(R2) | |
arg = (R-2)/0.1 | |
env1 = 1/(1+np.exp(arg)) | |
env2 = 1 - env1 | |
f = env2*(x*(1/(R-1.99)**2 + 1e-2) - x) + env1*(w*y + w*x*(1 - R)) | |
g = env2*(y*(1/(R-1.99)**2 + 1e-2) + y) + env1*(-w*x + w*y*(1 - R)) | |
return [f,g] | |
model_title = 'Steins Gate' | |
plt.figure() | |
xmin = lim[0] | |
xmax = lim[1] | |
ymin = lim[2] | |
ymax = lim[3] | |
plt.axis([xmin, xmax, ymin, ymax]) | |
N = 24*4 + 47 | |
x0 = np.zeros(shape=(N,2)) | |
ind = -1 | |
for i in range(0,24): | |
ind = ind + 1 | |
x0[ind,0] = xmin + (xmax-xmin)*i/23 | |
x0[ind,1] = ymin | |
ind = ind + 1 | |
x0[ind,0] = xmin + (xmax-xmin)*i/23 | |
x0[ind,1] = ymax | |
ind = ind + 1 | |
x0[ind,0] = xmin | |
x0[ind,1] = ymin + (ymax-ymin)*i/23 | |
ind = ind + 1 | |
x0[ind,0] = xmax | |
x0[ind,1] = ymin + (ymax-ymin)*i/23 | |
ind = ind + 1 | |
x0[ind,0] = 0.05 | |
x0[ind,1] = 0.05 | |
for thetloop in range(0,10): | |
ind = ind + 1 | |
theta = 2*np.pi*(thetloop)/10 | |
ys = 0.125*np.sin(theta) | |
xs = 0.125*np.cos(theta) | |
x0[ind,0] = xs | |
x0[ind,1] = ys | |
for thetloop in range(0,10): | |
ind = ind + 1 | |
theta = 2*np.pi*(thetloop)/10 | |
ys = 1.7*np.sin(theta) | |
xs = 1.7*np.cos(theta) | |
x0[ind,0] = xs | |
x0[ind,1] = ys | |
for thetloop in range(0,20): | |
ind = ind + 1 | |
theta = 2*np.pi*(thetloop)/20 | |
ys = 2*np.sin(theta) | |
xs = 2*np.cos(theta) | |
x0[ind,0] = xs | |
x0[ind,1] = ys | |
ind = ind + 1 | |
x0[ind,0] = -3 | |
x0[ind,1] = 0.05 | |
ind = ind + 1 | |
x0[ind,0] = -3 | |
x0[ind,1] = -0.05 | |
ind = ind + 1 | |
x0[ind,0] = 3 | |
x0[ind,1] = 0.05 | |
ind = ind + 1 | |
x0[ind,0] = 3 | |
x0[ind,1] = -0.05 | |
ind = ind + 1 | |
x0[ind,0] = -6 | |
x0[ind,1] = 0.00 | |
ind = ind + 1 | |
x0[ind,0] = 6 | |
x0[ind,1] = 0.00 | |
colors = plt.cm.prism(np.linspace(0, 1, N)) | |
# Solve for the trajectories | |
t = np.linspace(0, max_time, int(250*max_time)) | |
x_t = np.asarray([integrate.odeint(flow_deriv, x0i, t, param) | |
for x0i in x0]) | |
for i in range(N): | |
x, y = x_t[i,:,:].T | |
lines = plt.plot(x, y, '-', c=colors[i]) | |
plt.setp(lines, linewidth=1) | |
plt.show() | |
plt.title(model_title) | |
return t, x_t | |
param = (0.02,0.5,0.2) # Steins Gate | |
lim = (-6,6,-6,6) | |
t, x_t = solve_flow(param,lim) | |
plt.savefig('Steins Gate') |