GumowskiMira

Systems · Discrete · Exotic maps

Dimension: 2

Equations

\[ \begin{aligned} y_{0}' &= a y_{0} + b y_{1} + \frac{y_{0}^{2} \left(2 - 2 a\right)}{y_{0}^{2} + 1} \\ y_{1}' &= a \left(a y_{0} + b y_{1} + \frac{y_{0}^{2} \left(2 - 2 a\right)}{y_{0}^{2} + 1}\right) - y_{0} + \frac{\left(2 - 2 a\right) \left(a y_{0} + b y_{1} + \frac{y_{0}^{2} \left(2 - 2 a\right)}{y_{0}^{2} + 1}\right)^{2}}{\left(a y_{0} + b y_{1} + \frac{y_{0}^{2} \left(2 - 2 a\right)}{y_{0}^{2} + 1}\right)^{2} + 1} \end{aligned} \]

Parameters

parameter	default
a	-1.1
b	-0.2

Usage

import tsdynamics as ts

sys = ts.GumowskiMira()
traj = sys.iterate(steps=10_000)

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