SprottJ

Systems / ODEs / Chaotic attractors

Case J of Sprott's 1994 search for minimal chaotic flows — six terms with a single quadratic nonlinearity.

continuous · ODE3 dimensionschaotic

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Definition

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

Properties

Lyapunov spectrum

$+0.04486,\; +0.02563,\; -2.07$
computed at build

Kaplan–Yorke dimension

$D_{KY} = 2.034$

Divergence ∇·f

$\nabla\!\cdot f = -2$
constant

Equilibria

1 equilibria
0 stable · 1 unstable

Define it in TSDynamics

import tsdynamics as ts

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

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

Reference

Sprott (1994), Phys. Rev. E 50, R647-R650

BibTeX

@misc{sprottj,
  title = {SprottJ system},
  note = {Sprott (1994), Phys. Rev. E 50, R647-R650}
}