LorenzBounded

Systems · Continuous · Chaotic attractors

Dimension: 3

Equations

\[ \begin{aligned} \dot{y_{0}} &= - \sigma y_{0} + \sigma y_{1} + \frac{\sigma y_{0}^{3}}{r^{2}} - \frac{\sigma y_{0}^{2} y_{1}}{r^{2}} + \frac{\sigma y_{0} y_{1}^{2}}{r^{2}} + \frac{\sigma y_{0} y_{2}^{2}}{r^{2}} - \frac{\sigma y_{1}^{3}}{r^{2}} - \frac{\sigma y_{1} y_{2}^{2}}{r^{2}} \\ \dot{y_{1}} &= \rho y_{0} - y_{0} y_{2} - y_{1} - \frac{\rho y_{0}^{3}}{r^{2}} - \frac{\rho y_{0} y_{1}^{2}}{r^{2}} - \frac{\rho y_{0} y_{2}^{2}}{r^{2}} + \frac{y_{0}^{3} y_{2}}{r^{2}} + \frac{y_{0}^{2} y_{1}}{r^{2}} + \frac{y_{0} y_{1}^{2} y_{2}}{r^{2}} + \frac{y_{0} y_{2}^{3}}{r^{2}} + \frac{y_{1}^{3}}{r^{2}} + \frac{y_{1} y_{2}^{2}}{r^{2}} \\ \dot{y_{2}} &= - \beta y_{2} + \frac{\beta y_{0}^{2} y_{2}}{r^{2}} + \frac{\beta y_{1}^{2} y_{2}}{r^{2}} + \frac{\beta y_{2}^{3}}{r^{2}} + y_{0} y_{1} - \frac{y_{0}^{3} y_{1}}{r^{2}} - \frac{y_{0} y_{1}^{3}}{r^{2}} - \frac{y_{0} y_{1} y_{2}^{2}}{r^{2}} \end{aligned} \]

Parameters

parameter	default
beta	2.667
r	64
rho	28
sigma	10

Usage

import tsdynamics as ts

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

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