SprottJerk

Systems / ODEs / Chaotic attractors

The provably algebraically-simplest dissipative chaotic flow — a single-quadratic jerk system whose Möbius-strip attractor emerges by period doubling near mu ≈ 2.017.

continuous · ODE3 dimensionschaotic

Interactive: drag to rotate

Definition

\[ \begin{aligned} \dot{y_{0}} &= y_{1} \\ \dot{y_{1}} &= y_{2} \\ \dot{y_{2}} &= - \mu y_{2} - y_{0} + y_{1}^{2} \end{aligned} \]

Parameters

Symbol	Default	Role
mu	2.017	damping coefficient (chaos for 2.017 < mu < 2.082)

Properties

Lyapunov spectrum

TODO — Lyapunov compute exceeded 20s (killed)

Kaplan–Yorke dimension

TODO — requires a numeric Lyapunov spectrum

Divergence ∇·f

$\nabla\!\cdot f = - \mu$
constant

Equilibria

1 equilibria
0 stable · 1 unstable

Define it in TSDynamics

import tsdynamics as ts

sys = ts.systems.SprottJerk()
traj = sys.integrate(final_time=100.0, dt=0.01)

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

Reference

Sprott (1997), Phys. Lett. A 228, 271-274

BibTeX

@misc{sprottjerk,
  title = {SprottJerk system},
  note = {Sprott (1997), Phys. Lett. A 228, 271-274}
}