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

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

Properties

Lyapunov spectrum

$+0.09429,\; +0.004113,\; -0.6416$
computed at build

Kaplan–Yorke dimension

$D_{KY} = 2.153$

Divergence ∇·f

$\nabla\!\cdot f = y_{2} + 1$
state-dependent

Equilibria

2 equilibria
0 stable · 2 unstable

Define it in TSDynamics

import tsdynamics as ts

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

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

Reference

Pehlivan & Wei (2012), Turk. J. Electr. Eng. Comput. Sci. 20, 1229-1239

BibTeX

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