SprottMore

Systems / ODEs / Chaotic attractors

A minimal jerk flow built from non-polynomial elementary functions — sign-function Coulomb damping plus a Gaussian nonlinearity.

continuous · ODE3 dimensionschaotic

Interactive: drag to rotate

Definition

\[ \begin{aligned} \dot{x} &= y \\ \dot{y} &= - x - y \operatorname{sign}{\left(z \right)} \\ \dot{z} &= y^{2} - e^{- x^{2}} \end{aligned} \]

Properties

Lyapunov spectrum

TODO — lyapunov_spectrum failed: AttributeError

Kaplan–Yorke dimension

TODO — requires a numeric Lyapunov spectrum

Divergence ∇·f

n/a — non-smooth right-hand side — divergence is piecewise (defined almost everywhere)

Equilibria

none found (no equilibria)

Use it in TSDynamics

import tsdynamics as ts

system = ts.systems.SprottMore()
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 (2020), Chaos Theory Appl. 2, 1-3
doi:10.1016/j.chaos.2020.109990

BibTeX

@misc{sprottmore,
  title = {SprottMore system},
  note = {Sprott (2020), Chaos Theory Appl. 2, 1-3},
  doi = {10.1016/j.chaos.2020.109990}
}