Duffing

Systems · Continuous · Chaotic attractors

Dimension: 3

Equations

\[ \begin{aligned} \dot{y_{0}} &= y_{1} \\ \dot{y_{1}} &= - \alpha y_{0} - \beta y_{0}^{3} - \delta y_{1} + \gamma \cos{\left(y_{2} \right)} \\ \dot{y_{2}} &= \omega \end{aligned} \]

Parameters

parameter	default
alpha	1.0
beta	-1.0
delta	0.1
gamma	0.35
omega	1.4

Usage

import tsdynamics as ts

sys = ts.Duffing()
traj = sys.integrate(final_time=100.0, dt=0.01)

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