Gingerbreadman¶

Systems / Maps / Chaotic maps

A piecewise-linear map tiling the plane with quasiperiodic gingerbread-man cells.

discrete · map2 dimensionsquasiperiodic

Definition¶

\[ \begin{aligned} x' &= - y + \left|{x}\right| + 1 \\ y' &= x \end{aligned} \]

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

1 fixed points
0 stable · 1 unstable

Use it in TSDynamics¶

import tsdynamics as ts

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

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

Reference¶

Devaney (1984), Physica D 10, 387-393
doi:10.1016/0167-2789(84)90187-8

BibTeX

@misc{gingerbreadman,
  title = {Gingerbreadman system},
  note = {Devaney (1984), Physica D 10, 387-393},
  doi = {10.1016/0167-2789(84)90187-8}
}