ZeraouliaSprott¶

Systems / Maps / Exotic maps

A minimal 2-D rational map whose x-recurrence is a single non-vanishing fraction — one of the simplest rational maps reaching chaos via a quasi-periodic route.

discrete · map2 dimensionschaotic

Definition¶

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

Parameters¶

Symbol	Default	Role
`a`	`2.7`	gain of the rational x-recurrence (primary control parameter)
`b`	`0.35`	linear feedback coefficient of y

Properties¶

Lyapunov spectrum

$+0.00048,\; -0.602$
computed at build

Kaplan–Yorke dimension

$D_{KY} = 1.001$

Divergence ∇·f

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

Equilibria

1 fixed points
0 stable · 1 unstable

Define it in TSDynamics¶

import tsdynamics as ts

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

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

Reference¶

Zeraoulia & Sprott (2011), Int. J. Bifurcation Chaos 21, 155-160

BibTeX

@misc{zeraouliasprott,
  title = {ZeraouliaSprott system},
  note = {Zeraoulia & Sprott (2011), Int. J. Bifurcation Chaos 21, 155-160}
}