HyperYangChen¶

Systems / ODEs / Chaotic attractors

A four-dimensional Chen-like flow with an added linear feedback variable that yields hyperchaotic dynamics.

continuous · ODE4 dimensionshyperchaotic

projection (x, y, z)

projection (x, y, w)

Interactive: drag to rotate

Definition¶

\[ \begin{aligned} \dot{y_{0}} &= - a y_{0} + a y_{1} \\ \dot{y_{1}} &= c y_{0} - y_{0} y_{2} + y_{3} \\ \dot{y_{2}} &= - b y_{2} + y_{0} y_{1} \\ \dot{y_{3}} &= - d y_{0} \end{aligned} \]

Parameters¶

Symbol	Default	Role
`a`	`30`	flow coefficient
`b`	`3`	flow coefficient
`c`	`35`	flow coefficient
`d`	`8`	flow coefficient

Properties¶

Lyapunov spectrum

$+0.3724,\; +0.2484,\; -0.007866,\; -33.61$
computed at build

Kaplan–Yorke dimension

$D_{KY} = 3.018$

Divergence ∇·f

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

Equilibria

1 equilibria
0 stable · 1 unstable

Define it in TSDynamics¶

import tsdynamics as ts

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

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

Reference¶

Meier (2003), Presentation of Attractors with Cinema

BibTeX

@misc{hyperyangchen,
  title = {HyperYangChen system},
  note = {Meier (2003), Presentation of Attractors with Cinema}
}