如何生成陈氏超混沌序列。我曾尝试用python编写代码，但出现了一些问题。我得到了许多nan和infinity

Question

我想生成陈的超混沌序列。公式如下所示：Chen's hyperchaotic sequence equations

我写的代码附在后面

import math

a = 36
b = 3
c = 28
d = 16
k = 0.2


def chen(x0, y0, z0, q0):
    xdot = a * (y0 - x0)
    ydot = (-x0 * z0) + (d * x0) + (c * y0) - q0
    zdot = (x0 * y0) - (b * z0)
    qdot = x0 + k
    return xdot, ydot, zdot, qdot


def chaotic_seq(x0, y0, z0, q0, length):

    for i in range(length):
        xdot, ydot, zdot, qdot = chen(x0, y0, z0, q0)
        if math.isnan(xdot) or math.isnan(ydot) or math.isnan(zdot) or math.isnan(qdot):
            print(i)

        x0 = xdot
        y0 = ydot
        z0 = zdot
        q0 = qdot


if __name__ == '__main__':
    x0 = 0.3
    y0 = -0.4
    z0 = 1.2
    q0 = 1
    length = 2048
    chaotic_seq(x0=x0, y0=y0, z0=z0, q0=q0, length=length)

我面临的问题是，在“I=11”之后，所有值（xdot、ydot、zdot、qdot）都是NaN

Answer 1

您的代码远远没有达到您的期望：您将不得不在某个点上求解该微分方程，而在上面的示例中，您没有这样做。这就解释了为什么你的价值观会很快偏离到无穷远，然后开始变成“南”

使用scipy求解微分方程，我们得到以下代码，该代码给出了令人满意的结果：

from scipy.integrate import solve_ivp
import matplotlib.pyplot as plt

a = 36
b = 3
c = 12
d = 7
k = 0.2

def chen(_, y):
    x0, y0, z0, q0 = y
    xdot = a * (y0 - x0)
    ydot = (-x0 * z0) + (d * x0) + (c * y0) - q0
    zdot = (x0 * y0) - (b * z0)
    qdot = x0 + k
    return xdot, ydot, zdot, qdot


def chaotic_seq(x0, y0, z0, q0, length):
    return solve_ivp(chen, [0, length], [x0, y0, z0, q0])

x0 = 0.3
y0 = -0.4
z0 = 1.2
q0 = 1
length = 50
sol = chaotic_seq(x0=x0, y0=y0, z0=z0, q0=q0, length=length).y
# plot x,y
plt.plot(sol[0], sol[1])