SprottE

Systems / ODEs / Chaotic attractors

Case E 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

\[ \begin{aligned} \dot{x} &= y z \\ \dot{y} &= x^{2} - y \\ \dot{z} &= 1 - 4 x \end{aligned} \]

Properties

Lyapunov spectrum

TODO — lyapunov_spectrum failed: AttributeError

Kaplan–Yorke dimension

TODO — requires a numeric Lyapunov spectrum

Divergence ∇·f

$\nabla\!\cdot f = -1$
constant

Equilibria

1 equilibria
0 stable · 1 unstable

Use it in TSDynamics

import tsdynamics as ts

system = ts.systems.SprottE()
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 (1994), Phys. Rev. E 50, R647-R650
doi:10.1103/physreve.50.r647

BibTeX

@misc{sprotte,
  title = {SprottE system},
  note = {Sprott (1994), Phys. Rev. E 50, R647-R650},
  doi = {10.1103/physreve.50.r647}
}