GeneralizedHenon

Systems / Maps / Chaotic maps

The Baier-Klein 3-D generalization of the Hénon map — a single quadratic term chained through a delay line, exhibiting hyperchaos.

discrete · map3 dimensionshyperchaotic

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Definition

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

Parameters

Symbol	Default	Role
a	1.9	nonlinearity strength of the quadratic term
b	0.03	coupling to the delayed state (volume contraction rate)

Properties

Lyapunov spectrum

$+0.2772,\; +0.2591,\; -4.043$
computed at build

Kaplan–Yorke dimension

$D_{KY} = 2.133$

Divergence ∇·f

n/a — discrete map — flow divergence undefined (per-step contraction is |det J|)

Equilibria

2 fixed points
0 stable · 2 unstable

Define it in TSDynamics

import tsdynamics as ts

sys = ts.systems.GeneralizedHenon()
traj = sys.iterate(steps=10_000)

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

Reference

Baier & Klein (1990), Phys. Lett. A 151, 281-284

BibTeX

@misc{generalizedhenon,
  title = {GeneralizedHenon system},
  note = {Baier & Klein (1990), Phys. Lett. A 151, 281-284}
}