PehlivanWei

Systems / ODEs / Chaotic attractors

A parameter-free three-dimensional flow with two quadratic nonlinearities, notable for its simple algebraic form and equilibrium structure.

continuous · ODE3 dimensionschaotic

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Definition

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

Properties

Lyapunov spectrum

TODO — lyapunov_spectrum failed: AttributeError

Kaplan–Yorke dimension

TODO — requires a numeric Lyapunov spectrum

Divergence ∇·f

$\nabla\!\cdot f = z + 1$
state-dependent

Equilibria

2 equilibria
0 stable · 2 unstable

Use it in TSDynamics

import tsdynamics as ts

system = ts.systems.PehlivanWei()
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

Pehlivan & Wei (2012), Turk. J. Electr. Eng. Comput. Sci. 20, 1229-1239
doi:10.3906/elk-1103-14

BibTeX

@misc{pehlivanwei,
  title = {PehlivanWei system},
  note = {Pehlivan & Wei (2012), Turk. J. Electr. Eng. Comput. Sci. 20, 1229-1239},
  doi = {10.3906/elk-1103-14}
}