Bedhead

Systems / Maps / Exotic maps

An ornamental trigonometric attractor map.

discrete · map2 dimensionsattractor

attractor

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

Properties

Lyapunov spectrum

$+0.4765,\; -0.3625$
computed at build

Kaplan–Yorke dimension

$D_{KY} = 2$

Divergence ∇·f

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

Equilibria

32 fixed points
0 stable · 32 unstable

Define it in TSDynamics

import tsdynamics as ts

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

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