BurkeShaw

Systems / ODEs / Coupled systems

A symmetric chaotic flow derived from the Lorenz template.

continuous · ODE3 dimensionschaotic

Interactive: drag to rotate

Definition

\[ \begin{aligned} \dot{y_{0}} &= - n y_{0} - n y_{1} \\ \dot{y_{1}} &= - n y_{0} y_{2} + y_{1} \\ \dot{y_{2}} &= e + n y_{0} y_{1} \end{aligned} \]

Parameters

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

Properties

Lyapunov spectrum

$+2.253,\; +0.01336,\; -11.27$
computed at build

Kaplan–Yorke dimension

$D_{KY} = 2.201$

Divergence ∇·f

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

Equilibria

2 equilibria
0 stable · 2 unstable

Define it in TSDynamics

import tsdynamics as ts

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

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

Reference

Shaw (1981), Z. Naturforsch. A 36, 80-112

BibTeX

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