Bedhead¶

Systems / Maps / Exotic maps

An ornamental trigonometric attractor map.

discrete · map2 dimensionsattractor

Definition¶

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

Parameters¶

Symbol	Default	Role
`a`	`-0.67`	phase coefficient in the cos(a*x - y) term
`b`	`0.83`	scale dividing the x*y product and the sin(y) term

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

42 fixed points
0 stable · 42 unstable

Use it in TSDynamics¶

import tsdynamics as ts

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

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