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

Interactive: drag to rotate

Definition¶

\[ \begin{aligned} \dot{x} &= a \left(- x + y\right) \\ \dot{y} &= b x - c x z \\ \dot{z} &= - d z + e^{x y} \end{aligned} \]

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

State variables: x, y, z

Properties¶

Lyapunov spectrum

TODO — lyapunov_spectrum failed: AttributeError

Kaplan–Yorke dimension

TODO — requires a numeric Lyapunov spectrum

Divergence ∇·f

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

Equilibria

3 equilibria
0 stable · 3 unstable

Use it in TSDynamics¶

import tsdynamics as ts

system = ts.systems.YuWang()
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¶

Yu & Wang (2012), Eng. Technol. Appl. Sci. Res. 2, 209-215
doi:10.48084/etasr.86

BibTeX

@misc{yuwang,
  title = {YuWang system},
  note = {Yu & Wang (2012), Eng. Technol. Appl. Sci. Res. 2, 209-215},
  doi = {10.48084/etasr.86}
}