Svensson¶

Systems / Maps / Exotic maps

A trigonometric planar strange-attractor map whose sines and cosines trace intricate filamentary chaotic attractors.

discrete · map2 dimensionsattractor

Definition¶

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

Parameters¶

Symbol	Default	Role
`a`	`1.5`	angular frequency scaling x inside the trig terms
`b`	`-1.8`	angular frequency scaling y inside the trig terms
`c`	`1.6`	amplitude of the cosine contribution
`d`	`0.9`	amplitude of the sine contribution

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

3 fixed points
0 stable · 3 unstable

Use it in TSDynamics¶

import tsdynamics as ts

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

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