Torus

Systems · Continuous · Oscillatory systems

Dimension: 3

Equations

\[ \begin{aligned} \dot{y_{0}} &= - a n \sin{\left(n t \right)} \cos{\left(t \right)} - \left(a \cos{\left(n t \right)} + r\right) \sin{\left(t \right)} \\ \dot{y_{1}} &= - a n \sin{\left(t \right)} \sin{\left(n t \right)} + \left(a \cos{\left(n t \right)} + r\right) \cos{\left(t \right)} \\ \dot{y_{2}} &= a n \cos{\left(n t \right)} \end{aligned} \]

Parameters

parameter	default
a	0.5
n	15.3
r	1

Usage

import tsdynamics as ts

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

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