MooreSpiegel¶

Systems / ODEs / Oscillatory systems

A thermo-mechanical oscillator from stellar convection — aperiodic pulsation.

continuous · ODE3 dimensionschaotic

Interactive: drag to rotate

Definition¶

\[ \begin{aligned} \dot{x} &= y \\ \dot{y} &= a z \\ \dot{z} &= - b x + eps y - x^{2} y - z \end{aligned} \]

Parameters¶

Symbol	Default	Role
`a`	`10`	coupling / stiffness parameter
`b`	`4`	linear restoring parameter
`eps`	`9`	tension / heat-transfer parameter

State variables: x, y, z

Properties¶

Lyapunov spectrum

TODO — lyapunov_spectrum failed: AttributeError

Kaplan–Yorke dimension

TODO — requires a numeric Lyapunov spectrum

Divergence ∇·f

$\nabla\!\cdot f = -1$
constant

Equilibria

1 equilibria
0 stable · 1 unstable

Use it in TSDynamics¶

import tsdynamics as ts

system = ts.systems.MooreSpiegel()
traj = system.run(final_time=100.0, dt=0.01)
ts.plot(traj)

spectrum = ts.analysis.lyapunov_spectrum(system)
ts.analysis.kaplan_yorke_dimension(spectrum)

Reference¶

Moore & Spiegel (1966), Astrophys. J. 143, 871-887
doi:10.1086/148562

BibTeX

@misc{moorespiegel,
  title = {MooreSpiegel system},
  note = {Moore & Spiegel (1966), Astrophys. J. 143, 871-887},
  doi = {10.1086/148562}
}