SprottH

Systems / ODEs / Chaotic attractors

Case H of Sprott's 1994 search for minimal chaotic flows — six terms with a single quadratic nonlinearity.

continuous · ODE3 dimensionschaotic

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Definition

\[ \begin{aligned} \dot{y_{0}} &= - y_{1} + y_{2}^{2} \\ \dot{y_{1}} &= a y_{1} + y_{0} \\ \dot{y_{2}} &= y_{0} - y_{2} \end{aligned} \]

Parameters

Symbol	Default	Role
a	0.5	adjustable coefficient

Properties

Lyapunov spectrum

$+0.06975,\; -0.02154,\; -0.5482$
computed at build

Kaplan–Yorke dimension

$D_{KY} = 2.088$

Divergence ∇·f

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

Equilibria

2 equilibria
0 stable · 2 unstable

Define it in TSDynamics

import tsdynamics as ts

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

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

Reference

Sprott (1994), Phys. Rev. E 50, R647-R650

BibTeX

@misc{sprotth,
  title = {SprottH system},
  note = {Sprott (1994), Phys. Rev. E 50, R647-R650}
}