DeJong¶

Systems / Maps / Polynomial maps

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

discrete · map2 dimensionsattractor

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

State variables: x, y

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

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

Reference¶

Dewdney (1987), Scientific American 257(1), 108-111
doi:10.1038/scientificamerican0787-108

BibTeX

@misc{dejong,
  title = {DeJong system},
  note = {Dewdney (1987), Scientific American 257(1), 108-111},
  doi = {10.1038/scientificamerican0787-108}
}