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.
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)
