BurkeShaw

Systems / ODEs / Coupled systems

A symmetric chaotic flow derived from the Lorenz template.

continuous · ODE3 dimensionschaotic

Interactive: drag to rotate

Definition

\[ \begin{aligned} \dot{x} &= - n x - n y \\ \dot{y} &= - n x z + y \\ \dot{z} &= e + n x y \end{aligned} \]

Parameters

Symbol	Default	Role
e	13	constant forcing on the z channel
n	10	common coupling / timescale scaling the cross terms

State variables: x, y, z

Properties

Lyapunov spectrum

TODO — lyapunov_spectrum failed: AttributeError

Kaplan–Yorke dimension

TODO — requires a numeric Lyapunov spectrum

Divergence ∇·f

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

Equilibria

2 equilibria
0 stable · 2 unstable

Use it in TSDynamics

import tsdynamics as ts

system = ts.systems.BurkeShaw()
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

Shaw (1981), Z. Naturforsch. A 36, 80-112
doi:10.1515/zna-1981-0115

BibTeX

@misc{burkeshaw,
  title = {BurkeShaw system},
  note = {Shaw (1981), Z. Naturforsch. A 36, 80-112},
  doi = {10.1515/zna-1981-0115}
}