DequanLi

Systems / ODEs / Coupled systems

A Lorenz-family quadratic flow whose extra x*z and x**2 terms break the two-scroll structure into a three-scroll attractor.

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	40	x–y channel coupling gain
c	1.833	self-feedback gain of the z channel
d	0.16	x*z cross-product strength in the x equation
eps	0.65	x**2 term strength in the z equation
f	20	self-feedback gain of the y channel
k	55	forcing gain of the y channel

State variables: x, y, z

Properties

Lyapunov spectrum

TODO — lyapunov_spectrum failed: AttributeError

Kaplan–Yorke dimension

TODO — requires a numeric Lyapunov spectrum

Divergence ∇·f

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

Equilibria

1 equilibria
0 stable · 1 unstable

Use it in TSDynamics

import tsdynamics as ts

system = ts.systems.DequanLi()
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

Li (2008), Phys. Lett. A 372, 387-393
doi:10.1016/j.physleta.2007.07.045

BibTeX

@misc{dequanli,
  title = {DequanLi system},
  note = {Li (2008), Phys. Lett. A 372, 387-393},
  doi = {10.1016/j.physleta.2007.07.045}
}