Python+Scipyでルンゲクッタ8次のDOP853(Dormand Prince)を使う（その3） Aizawa Attractor

今回はみかん袋（あみあみ）を丸めたようなAizawa attractor。

http://analog-ontology.blogspot.com/2015/06/the-aizawa-attractor-iv.html

dx/dt = (z-b)*x - d*y
dy/dt = d*x+(z-b)*y
dz/dt = c+a*z-(z^3)/3 - (x^2 +y^2)*(1+e*z)+f*z*x^3

のような形で、計算結果はこちら。

プログラムはこんな感じで。

import numpy as np
from scipy.integrate import ode
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

def aizawa(t, x, a, b, c, d, e, f): #odeintのときとt,xの並びが逆
    x_dot = (x[2]-b)*x[0] - d*x[1]
    y_dot = d*x[0]+(x[2]-b)*x[1]
    z_dot = c+a*x[2]-(x[2]**3)/3 - (x[0]**2 +x[1]**2)*(1+e*x[2])+f*x[2]*x[0]**3
    return [x_dot, y_dot, z_dot]

t0=0
tmax = 1000
N=100000

x0=[0.1, 0.0, 0.0]
solver=ode(aizawa)
solver.set_integrator('dop853')
solver.set_initial_value(x0,t0) #なぜか関数と並びが逆
solver.set_f_params(0.95,0.7,0.6,3.5,0.25,0.1)

t=np.linspace(0, tmax, N)
sol= np.empty((N, 3))
sol[0] = x0

k=1
while solver.successful() and solver.t < tmax:
    solver.integrate(t[k]) 
    sol[k] = solver.y
    k+= 1

# Plot
fig = plt.figure(figsize=(12,12))
ax = fig.gca(projection='3d')

ax.plot(sol[:,0], sol[:,1], sol[:,2], lw=0.5)
ax.set_xlabel("X Axis")
ax.set_ylabel("Y Axis")
ax.set_zlabel("Z Axis")
ax.set_title("Aizawa Attractor(DOP853)")

plt.show()