PanXuZhou¶

Systems / ODEs / Coupled systems

A compact single-scroll chaotic attractor in the Dequan-Li family at the Pan–Xu–Zhou parameters, where the x·z and x² terms switch off.

continuous · ODE3 dimensionschaotic

Interactive: drag to rotate

Definition¶

\[ \begin{aligned} \dot{y_{0}} &= - a y_{0} + a y_{1} + d y_{0} y_{2} \\ \dot{y_{1}} &= f y_{1} + k y_{0} - y_{0} y_{2} \\ \dot{y_{2}} &= c y_{2} - eps y_{0}^{2} + y_{0} y_{1} \end{aligned} \]

Parameters¶

Symbol	Default	Role
`a`	`10`	x–y coupling gain
`c`	`-2.6667`	z self-feedback
`d`	`0`	x·z term strength
`eps`	`0`	x² term strength
`f`	`0`	y self-feedback
`k`	`16`	y forcing gain

Properties¶

Lyapunov spectrum

$+0.6263,\; +0.003171,\; -13.3$
computed at build

Kaplan–Yorke dimension

$D_{KY} = 2.047$

Divergence ∇·f

$\nabla\!\cdot f = - a + c + d y_{2} + f$
state-dependent

Equilibria

3 equilibria
2 stable · 1 unstable

Define it in TSDynamics¶

import tsdynamics as ts

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

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

Reference¶

Zhou, Wuneng et al. (2008), Phys. Lett. A 372, 5773-5777

BibTeX

@misc{panxuzhou,
  title = {PanXuZhou system},
  note = {Zhou, Wuneng et al. (2008), Phys. Lett. A 372, 5773-5777}
}