anthony-dipofi / chaoticattractors

Chaotic Attractors

A library to simulate trajectories of various systems of differential and difference equations, built primarily for the purpose of exploring the dynamics of chaotic attractors. Requires Numpy and Matplotlib.

Examples

Rabinovich–Fabrikant equations

https://en.wikipedia.org/wiki/Rabinovich%E2%80%93Fabrikant_equations

from attractors import RabFab_attractor
RabFab_attractor(init = (-1,0,0.5), a = 1.1, g = 0.87, speed = 0.001, steps = 150000)

RabFab_attractor(init = (-1,0,0.5), a = 0.14, g = 0.1, speed = 0.001, steps = 350000)

Rossler Attractor

https://en.wikipedia.org/wiki/R%C3%B6ssler_attractor

from attractors import Rossler_attractor
Rossler_attractor(init = (0.1,0.1,0.1), a = 0.35, b = 0.5, c = 12, speed = 0.01, steps = 15000)

Lu Chen Attractor

https://en.wikipedia.org/wiki/Multiscroll_attractor

from attractors import Lu_Chen_attractor
Lu_Chen_attractor(init = (0.1, 0.3, -0.5), a = 29, b = 3, c = 22, u = -1, speed = 0.001, steps = 25000) 

Skew Tent Map

https://infoscience.epfl.ch/record/52235/files/IC_TECH_REPORT_199704.pdf

from attractors import Skew_Tent_map
Skew_Tent_map(init = 0.5, b = 0.68, steps = 250)

Logistic Map

https://en.wikipedia.org/wiki/Logistic_map

from attractors import Logistic_map
Logistic_map(init = 0.5, p = 3.99, steps = 150)

Logistic_map(init = 0.5, p = 3.75, steps = 300)

Gingerbread Map

http://mathworld.wolfram.com/GingerbreadmanMap.html

from attractors import GingerBread_map
GingerBread_map(init = (3.5, 3.5), steps = 250)

Van der Pol Oscillator

https://arxiv.org/abs/0803.1658

from attractors import VanDerPol_oscillator
VanDerPol_oscillator(init = (0.5, 0.5), p = 1.614, speed = 0.001, steps = 15250)

Bogdanov Map

https://arxiv.org/abs/chao-dyn/9402006

from attractors import Bogdanov_map
Bogdanov_map(init=(0.1,0), epsilon = 0.0000, k = 0.0001, mu = 0.020, steps = 10450)

Lorenz Attractor

https://en.wikipedia.org/wiki/Lorenz_system

from attractors import Lorenz_attractor
Lorenz_attractor(init = (10,10,10), sigma = 10, rho = 28, beta = 8/3, speed = 0.001, steps = 30000)