PanXuZhou¶

Systems / ODEs / Coupled systems

A two-scroll, Lorenz-like chaotic attractor in the Dequan-Li family at the Pan–Xu–Zhou parameters, where the x·z and x² terms switch off. The catalogue ships k = 28 rather than the paper's k = 16: the published value lies below the Hopf threshold k ≈ 17.27, where the orbit settles onto a stable focus instead of sustaining chaos.

continuous · ODE3 dimensionschaotic

Interactive: drag to rotate

Definition¶

\[ \begin{aligned} \dot{x} &= - a x + a y + d x z \\ \dot{y} &= f y + k x - x z \\ \dot{z} &= c z - eps x^{2} + x y \end{aligned} \]

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`	`28`	y forcing gain

State variables: x, y, z

Properties¶

Lyapunov spectrum

$+1,\; 0,\; -13.67$
measured; the sum is pinned analytically by the constant divergence -(a - f) + c = -12.667

Kaplan–Yorke dimension

$D_{KY} = 2.073$

Divergence ∇·f

$\nabla\!\cdot f = - a + c + d z + f$
state-dependent

Equilibria

3 equilibria
0 stable · 3 unstable

Use it in TSDynamics¶

import tsdynamics as ts

system = ts.systems.PanXuZhou()
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¶

Zhou, Wuneng et al. (2008), Phys. Lett. A 372, 5773-5777
doi:10.1016/j.physleta.2008.07.032

BibTeX

@misc{panxuzhou,
  title = {PanXuZhou system},
  note = {Zhou, Wuneng et al. (2008), Phys. Lett. A 372, 5773-5777},
  doi = {10.1016/j.physleta.2008.07.032}
}