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¶

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

Parameters¶

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

State variables: x, y, z

Properties¶

Lyapunov spectrum

TODO — lyapunov_spectrum failed: AttributeError

Kaplan–Yorke dimension

TODO — requires a numeric Lyapunov spectrum

Divergence ∇·f

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

Equilibria

2 fixed points
0 stable · 2 unstable

Use it in TSDynamics¶

import tsdynamics as ts

system = ts.systems.GeneralizedHenon()
traj = system.run(steps=10_000)
ts.plot(traj)

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

Reference¶

Baier & Klein (1990), Phys. Lett. A 151, 281-284
doi:10.1016/0375-9601(90)90283-t

BibTeX

@misc{generalizedhenon,
  title = {GeneralizedHenon system},
  note = {Baier & Klein (1990), Phys. Lett. A 151, 281-284},
  doi = {10.1016/0375-9601(90)90283-t}
}