chaztikov/chaospy-1

Chaotic attractors (Lorenz, Rossler, Rikitake etc.) and their features and properties

Chaotic attractors

Python scripts for some 3rd order chaotic systems (Lorenz attractor, Nose-Hoover oscillator, Rossler attractor, Riktake model)

License: GNU GPL 3.0.

Info:

Title	Analysis and modeling chaotic systems
Author	Alexander Kapitanov
Contact	[email protected]
Project lang	Python
Libraries	Numpy, Scipy, etc.
First Release	30 May 2019
Version	1.0

List of chaotic 3D systems:

Lorenz

dx/dt = sigma * (y - x)
dy/dt = rho * (x - z) - y
dz/dt = x * y - beta * z

where sigma= 10, rho= 28 and beta= 8/3.

Rossler 3D system

dx/dt = -(y + z)
dy/dt = x + a * y
dz/dt = b + z * (x - c)

where a = 0.2, b = 0.2 and c = 5.7.

Rikitake

dx/dt = -mu * x + z * y
dy/dt = -mu * y + x * (z - a)
dz/dt = 1 - x * y

where mu = 1, a = 5.

Nose–Hoover

dx/dt = y
dy/dt = y * z - x
dz/dt = 1 - y^2

Nose-Hoover doesn't have default parameters.

Wang system

dx/dt = x - y * z
dy/dt = x - y + x * z
dz/dt = -3 * z + x * y

Duffing map

dx/dt = y
dy/dt = -a * y - x**3 + b * cos(z)
dz/dt = 1

where a = 0.1 and b = 11.

Lotka–Volterra

dx/dt = x * (1 - x - 9*y)
dy/dt = -y * (1 - 6*x - y + 9*z)
dz/dt = z * (1 - 3*x - z)

Chua

dx/dt = alpha * (y - x - h(t))
dy/dt = x - y + z
dz/dt = -beta * y

ht = mu1*x + 0.5*(mu0 - mu1)*(np.abs(x + 1) - np.abs(x - 1))

where alpha = 15.6, beta = 28, mu0 = -1.143, mu1 = -0.714.

See more: Wikipedia about attractors

My topics (Russian lang.): https://habr.com/users/capitanov/topics/