SanUmSrisuchinwong

Systems / ODEs / Coupled systems

A single-parameter chaotic flow built from just a z*tanh(x) term, a quadratic x*y product, and an abs(y) term — convenient for analogue-circuit realisation.

continuous · ODE3 dimensionschaotic

Interactive: drag to rotate

Definition

\[ \begin{aligned} \dot{y_{0}} &= - y_{0} + y_{1} \\ \dot{y_{1}} &= - y_{2} \tanh{\left(y_{0} \right)} \\ \dot{y_{2}} &= - a + y_{0} y_{1} + \left|{y_{1}}\right| \end{aligned} \]

Parameters

Symbol	Default	Role
a	2	constant forcing on the z channel (the single tunable parameter)

Properties

Lyapunov spectrum

$+0.2251,\; +0.01041,\; -1.236$
computed at build

Kaplan–Yorke dimension

$D_{KY} = 2.191$

Divergence ∇·f

$\nabla\!\cdot f = -1$
constant

Equilibria

2 equilibria
0 stable · 2 unstable

Define it in TSDynamics

import tsdynamics as ts

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

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

Reference

San-Um & Srisuchinwong (2012), J. Comput. 7, 1041-1047

BibTeX

@misc{sanumsrisuchinwong,
  title = {SanUmSrisuchinwong system},
  note = {San-Um & Srisuchinwong (2012), J. Comput. 7, 1041-1047}
}