DeJong

Systems / Maps / Polynomial maps

A Peter de Jong attractor — a sinusoidal iterated map prized for its lacework structure.

discrete · map2 dimensionsattractor

attractor

Definition

@staticmethod
def _step(X, a, b, c, d):
    x, y = X
    xp = np.sin(a * y) - np.cos(b * x)
    yp = np.sin(c * x) - np.cos(d * y)
    return xp, yp

Parameters

Symbol	Default	Role
a	1.641	map parameter selecting attractor geometry
b	1.902	map parameter selecting attractor geometry
c	0.316	map parameter selecting attractor geometry
d	1.525	map parameter selecting attractor geometry

Properties

Lyapunov spectrum

$+0.2824,\; -0.5809$
computed at build

Kaplan–Yorke dimension

$D_{KY} = 1.486$

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.DeJong()
traj = sys.iterate(steps=10_000)

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

Reference

Dewdney (1987), Scientific American 257(1), 108-111

BibTeX

@misc{dejong,
  title = {DeJong system},
  note = {Dewdney (1987), Scientific American 257(1), 108-111}
}