MooreSpiegel¶

Systems / ODEs / Oscillatory systems

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

continuous · ODE3 dimensionschaotic

Interactive: drag to rotate

Definition¶

\[ \begin{aligned} \dot{y_{0}} &= y_{1} \\ \dot{y_{1}} &= a y_{2} \\ \dot{y_{2}} &= - b y_{0} + eps y_{1} - y_{0}^{2} y_{1} - y_{2} \end{aligned} \]

Parameters¶

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

Properties¶

Lyapunov spectrum

$+0.111,\; -0.004601,\; -1.106$
computed at build

Kaplan–Yorke dimension

$D_{KY} = 2.096$

Divergence ∇·f

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

Equilibria

1 equilibria
0 stable · 1 unstable

Define it in TSDynamics¶

import tsdynamics as ts

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

exps = sys.lyapunov_spectrum()
ts.kaplan_yorke_dimension(exps)

Reference¶

Moore & Spiegel (1966), Astrophys. J. 143, 871-887

BibTeX

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