Math 123 Chaotic system

In [4]:
## cite wikipedia
import numpy as np
import matplotlib.pyplot as plt
from scipy.integrate import odeint
from mpl_toolkits.mplot3d import Axes3D

rho = 28.0
sigma = 10.0
beta = 8.0 / 3.0

def f(state, t):
  x, y, z = state  # unpack the state vector
  return sigma * (y - x), x * (rho - z) - y, x * y - beta * z  # derivatives

state0 = [1.0, 1.0, 1.0]
t = np.arange(0.0, 40.0, 0.01)

states = odeint(f, state0, t)

fig = plt.figure()
ax = fig.gca(projection='3d')
ax.plot(states[:,0], states[:,1], states[:,2])
plt.show()
In [3]:
state0 = [1.0, 1.0, 1.0001]
t = np.arange(0.0, 40.0, 0.01)

states1 = odeint(f, state0, t)

fig = plt.figure()
ax = fig.gca(projection='3d')
ax.plot(states[:,0], states1[:,1], states1[:,2])
plt.show()
In [19]:
states[-1]-states1[-1]
Out[19]:
array([ -9.17879213,  -4.98955832, -18.79269286])