YuWang

Systems / ODEs / Coupled systems

A Yu–Wang flow whose z equation carries a quadratic-exponential exp(x*y) nonlinearity, yielding a compound mirror-merged attractor unlike the purely quadratic Lorenz family.

continuous · ODE3 dimensionschaotic

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Definition

\[ \begin{aligned} \dot{y_{0}} &= a \left(- y_{0} + y_{1}\right) \\ \dot{y_{1}} &= b y_{0} - c y_{0} y_{2} \\ \dot{y_{2}} &= - d y_{2} + e^{y_{0} y_{1}} \end{aligned} \]

Parameters

Symbol	Default	Role
a	10	x–y channel coupling gain
b	40	forcing gain of x into y
c	2	x*z cross-product strength in the y equation
d	2.5	linear decay rate of the z channel

Properties

Lyapunov spectrum

$+1.428,\; -0.008028,\; -13.92$
computed at build

Kaplan–Yorke dimension

$D_{KY} = 2.102$

Divergence ∇·f

$\nabla\!\cdot f = - a - d$
constant

Equilibria

3 equilibria
0 stable · 3 unstable

Define it in TSDynamics

import tsdynamics as ts

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

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

Reference

Yu & Wang (2012), Eng. Technol. Appl. Sci. Res. 2, 209-215

BibTeX

@misc{yuwang,
  title = {YuWang system},
  note = {Yu & Wang (2012), Eng. Technol. Appl. Sci. Res. 2, 209-215}
}