Exploring Chaotic Attractors in Jupyter Lab - Aizawa Attractor

In [45]:

%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
# This import registers the 3D projection, but is otherwise unused.
from mpl_toolkits.mplot3d import Axes3D  # noqa: F401 unused import


def aizawa(x, y, z, a=0.95, b=0.7, c=0.1,d=3.5,e=0.25,g=0.6):
    '''
    Given:
       x, y, z: a point of interest in three dimensional space
       s, r, b: parameters defining the lorenz attractor
    Returns:
       x_dot, y_dot, z_dot: values of the lorenz attractor's partial
           derivatives at the point x, y, z
    '''
    x_dot = (z-b)*x - d*y
    y_dot = d*x + (z - b)*y
    z_dot = g + a*z - ((z**3)/3) - ((x**2) + (y**2))*(1 + e*z) + c*z*(x**3)
    
    return x_dot, y_dot, z_dot


dt = 0.01
num_steps = 7000

# Need one more for the initial values
xs = np.empty(num_steps + 1)
ys = np.empty(num_steps + 1)
zs = np.empty(num_steps + 1)

# Set initial values
xs[0], ys[0], zs[0] = (0.1, 0, 0.1)

# Step through "time", calculating the partial derivatives at the current point
# and using them to estimate the next point
for i in range(num_steps):
    x_dot, y_dot, z_dot = aizawa(xs[i], ys[i], zs[i])
    xs[i + 1] = xs[i] + (x_dot * dt)
    ys[i + 1] = ys[i] + (y_dot * dt)
    zs[i + 1] = zs[i] + (z_dot * dt)


# Plot
fig = plt.figure()
ax = fig.gca(projection='3d')

ax.plot(xs, ys, zs, lw=0.5)
ax.set_xlabel("X Axis")
ax.set_ylabel("Y Axis")
ax.set_zlabel("Z Axis")
ax.set_title("Aizawa Plot")

plt.show()

plt.plot(xs)

Out[45]:

[<matplotlib.lines.Line2D at 0xae304d2c>]

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