我正在尝试绘制 Hindmarsh-Rose 模型的相空间轨迹。我已经实现了一个 RK4 积分器来求解以下方程组：
到目前为止，我编写的代码如下所示。
import numpy as np
import matplotlib.pyplot as plt
def RK4(f, x0, t):
dt = t[2] -t[1] #time span
N = len(t)
X = np.empty((len(t), len(x0)))
X[0] = x0
for i in range(1, N):
k1 = f(X[i-1], t[i-1])
k2 = f(X[i-1] + dt/2*k1, t[i-1] + dt/2)
k3 = f(X[i-1] + dt/2*k2, t[i-1] + dt/2)
k4 = f(X[i-1] + dt*k3, t[i-1] + dt)
X[i] = X[i-1] + dt/6*(k1 + 2*k2 + 2*k3 + k4)
return X
def hindmarsh(X, t):
a = 3.0
c = 1.0
d = 5.0
s = 4.0
x0 = - 1.6
# Bifurcation parameters
b = 3.09
I = 3.2
eps = 0.001
x,y,z = X
dxdt = y - (a * x**3) + (b * x**2) + I - z
dydt = c - (d * x**2) - y
dzdt = eps * ( (s * (x - x0)) - z)
return np.array([dxdt, dydt, dzdt])
T = np.linspace(0,100,10000)
Y = [0.03, 0.03, 3]
param = RK4( hindmarsh, Y, T )
ax = plt.axes(projection='3d')
zline = param[2]
yline = param[1]
xline = param[0]
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_zlabel('z')
ax.plot3D(xline, yline, zline)
但是，我没有在相位空间中获得如下图所示的轨道，而是在相位空间中获得了一条直线。我将不胜感激有关如何获得下面的情节的任何提示。
