SprottP

Systems / ODEs / Chaotic attractors

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

continuous · ODE3 dimensionschaotic

Interactive: drag to rotate

Definition

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

Parameters

Symbol	Default	Role
a	2.7	adjustable coefficient

State variables: x, y, z

Properties

Lyapunov spectrum

TODO — lyapunov_spectrum failed: AttributeError

Kaplan–Yorke dimension

TODO — requires a numeric Lyapunov spectrum

Divergence ∇·f

$\nabla\!\cdot f = 2 y$
state-dependent

Equilibria

2 equilibria
0 stable · 2 unstable

Use it in TSDynamics

import tsdynamics as ts

system = ts.systems.SprottP()
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{sprottp,
  title = {SprottP system},
  note = {Sprott (1994), Phys. Rev. E 50, R647-R650},
  doi = {10.1103/physreve.50.r647}
}