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

\[ \begin{aligned} \dot{y_{0}} &= y_{1} \\ \dot{y_{1}} &= - y_{0} - y_{1} \operatorname{sign}{\left(y_{2} \right)} \\ \dot{y_{2}} &= y_{1}^{2} - e^{- y_{0}^{2}} \end{aligned} \]

Properties

Lyapunov spectrum

$+0.01694,\; +0.01147,\; -0.046$
computed at build

Kaplan–Yorke dimension

$D_{KY} = 2.618$

Divergence ∇·f

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

Equilibria

none found (no equilibria)

Define it in TSDynamics

import tsdynamics as ts

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

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

Reference

Sprott (2020), Chaos Theory Appl. 2, 1-3

BibTeX

@misc{sprottmore,
  title = {SprottMore system},
  note = {Sprott (2020), Chaos Theory Appl. 2, 1-3}
}