DoubleGyre

Systems · Continuous · Climate geophysics

Dimension: 3

Equations

\[ \begin{aligned} \dot{y_{0}} &= - \pi \alpha \sin{\left(\pi \left(eps y_{0}^{2} \sin{\left(y_{2} \right)} + y_{0} \left(- 2 eps \sin{\left(y_{2} \right)} + 1\right)\right) \right)} \cos{\left(\pi y_{1} \right)} \\ \dot{y_{1}} &= \pi \alpha \left(2 eps y_{0} \sin{\left(y_{2} \right)} - 2 eps \sin{\left(y_{2} \right)} + 1\right) \sin{\left(\pi y_{1} \right)} \cos{\left(\pi \left(eps y_{0}^{2} \sin{\left(y_{2} \right)} + y_{0} \left(- 2 eps \sin{\left(y_{2} \right)} + 1\right)\right) \right)} \\ \dot{y_{2}} &= \omega \end{aligned} \]

Parameters

parameter	default
alpha	0.1
eps	0.1
omega	0.62832

Usage

import tsdynamics as ts

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

Back to Climate geophysics