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

\[ \begin{aligned} \dot{x} &= y \\ \dot{y} &= z \\ \dot{z} &= - \mu z - x + y^{2} \end{aligned} \]

Parameters

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

State variables: x, y, z

Properties

Lyapunov spectrum

TODO — lyapunov_spectrum failed: AttributeError

Kaplan–Yorke dimension

TODO — requires a numeric Lyapunov spectrum

Divergence ∇·f

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

Equilibria

1 equilibria
0 stable · 1 unstable

Use it in TSDynamics

import tsdynamics as ts

system = ts.systems.SprottJerk()
traj = system.run(final_time=100.0, dt=0.01)
ts.plot(traj)

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

Reference

Sprott (1997), Phys. Lett. A 228, 271-274
doi:10.1016/s0375-9601(97)00088-1

BibTeX

@misc{sprottjerk,
  title = {SprottJerk system},
  note = {Sprott (1997), Phys. Lett. A 228, 271-274},
  doi = {10.1016/s0375-9601(97)00088-1}
}