GenesioTesi¶

Systems / ODEs / Chaotic attractors

A canonical jerk control system whose single quadratic nonlinearity, analysed by harmonic balance, produces a Shilnikov strange attractor.

continuous · ODE3 dimensionschaotic

Interactive: drag to rotate

Definition¶

\[ \begin{aligned} \dot{x} &= y \\ \dot{y} &= z \\ \dot{z} &= - a z - b y - c x + x^{2} \end{aligned} \]

Parameters¶

Symbol	Default	Role
`a`	`0.44`	acceleration feedback gain
`b`	`1.1`	velocity feedback gain
`c`	`1`	position feedback gain

State variables: x, y, z

Properties¶

Lyapunov spectrum

$+0.1222,\; -0.003065,\; -0.5592$
computed at build

Kaplan–Yorke dimension

$D_{KY} = 2.213$

Divergence ∇·f

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

Equilibria

2 equilibria
0 stable · 2 unstable

Define it in TSDynamics¶

import tsdynamics as ts

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

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

Reference¶

Genesio & Tesi (1992), Automatica 28, 531-548

BibTeX

@misc{genesiotesi,
  title = {GenesioTesi system},
  note = {Genesio & Tesi (1992), Automatica 28, 531-548}
}