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

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

Parameters

Symbol	Default	Role
a	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

Properties

Lyapunov spectrum

$+0.005696,\; -0.17,\; -1.54$
computed at build

Kaplan–Yorke dimension

$D_{KY} = 1.034$

Divergence ∇·f

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

Equilibria

1 equilibria
0 stable · 1 unstable

Define it in TSDynamics

import tsdynamics as ts

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

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

Reference

Li (2008), Phys. Lett. A 372, 387-393

BibTeX

@misc{dequanli,
  title = {DequanLi system},
  note = {Li (2008), Phys. Lett. A 372, 387-393}
}