SprottD

Systems / ODEs / Chaotic attractors

Case D of Sprott's 1994 search for the algebraically simplest chaotic flows — five terms and two quadratic nonlinearities.

continuous · ODE3 dimensionschaotic

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Definition

\[ \begin{aligned} \dot{y_{0}} &= - y_{1} \\ \dot{y_{1}} &= y_{0} + y_{2} \\ \dot{y_{2}} &= y_{0} y_{2} + 3 y_{1}^{2} \end{aligned} \]

Properties

Lyapunov spectrum

$+0.09569,\; -0.008245,\; -1.283$
computed at build

Kaplan–Yorke dimension

$D_{KY} = 2.068$

Divergence ∇·f

$\nabla\!\cdot f = y_{0}$
state-dependent

Equilibria

2 equilibria
0 stable · 2 unstable

Define it in TSDynamics

import tsdynamics as ts

sys = ts.systems.SprottD()
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{sprottd,
  title = {SprottD system},
  note = {Sprott (1994), Phys. Rev. E 50, R647-R650}
}