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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

\[ \begin{aligned} \dot{x} &= - x + y \\ \dot{y} &= - z \tanh{\left(x \right)} \\ \dot{z} &= - a + x y + \left|{y}\right| \end{aligned} \]

Parameters

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

State variables: x, y, z

Properties

Lyapunov spectrum
TODO — lyapunov_spectrum failed: AttributeError
Kaplan–Yorke dimension
TODO — requires a numeric Lyapunov spectrum
Divergence ∇·f
$\nabla\!\cdot f = -1$
constant
Equilibria
2 equilibria
0 stable · 2 unstable

Use it in TSDynamics

import tsdynamics as ts

system = ts.systems.SanUmSrisuchinwong()
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

San-Um & Srisuchinwong (2012), J. Comput. 7, 1041-1047
doi:10.4304/jcp.7.4.1041-1047

BibTeX 
@misc{sanumsrisuchinwong,
  title = {SanUmSrisuchinwong system},
  note = {San-Um & Srisuchinwong (2012), J. Comput. 7, 1041-1047},
  doi = {10.4304/jcp.7.4.1041-1047}
}