Question:

How do I simulate differential jerk systems in Python?

Problem:

I am a beginner in Python, and I'm trying to simulate a multi scroll chaotic attractor for a project. The details and parameters are in >https://sci-hub.se/10.1142/s0218127420501862 [3.2 (i)]

I'm getting an empty plot. Any help would be greatly appreciated. I have tried the ODEINT method for solving the equations.

def system(state, t, alpha):

x1, x2, x3, x4, x5, x6 = state

dxdt = [

x2,

x3,

x4,

x5,

x6,

alpha[0] * (f(x1) - x1) - alpha[1] * x2 - alpha[2] * x3 - alpha[3] * x4 - alpha[4] * x5 - alpha[5] * x6

]

return dxdt

# Define the nonlinear function f(x)

def f(x):

M = 1

e = 1

q = 0.01

return (e / (2 * q)) * sum([np.abs(x - 2 * m * e + q) - np.abs(x - 2 * m * e - q) for m in range(-M, M + 1)])

# Set parameters

alpha_values = [7.5, 10, 10, 40, 10, 10]

initial_state = [0, 0, 0, 0, 0, 0]

time = np.linspace(0, 100, 10000)

# Solve ODEs

solution = odeint(system, initial_state, time, args=(alpha_values,))

Solution:

Well, here you go. The major problem with your code seems to be the initial values (it really doesn't like all zeroes). There is some sensitivity to the parameter R (I found the paper you are alluding to in the end). You also need a solution to a larger Tmax.

Link to paper: >https://doi.org/10.1142/S0218127420501862 but I'm relying on university access to that - it may not be an open-access paper.

import numpy as np

from scipy.integrate import odeint

def system(state, t, alpha):

x1, x2, x3, x4, x5, x6 = state

dxdt = [

x2,

x3,

x4,

x5,

x6,

alpha[0] * (f(x1) - x1) - alpha[1] * x2 - alpha[2] * x3 - alpha[3] * x4 - alpha[4] * x5 - alpha[5] * x6