SprottA

Systems / ODEs / Chaotic attractors

Case A of Sprott's 1994 minimal-chaos search — a five-term conservative flow identical to the Nosé–Hoover thermostat, its chaotic sea threaded with invariant tori.

continuous · ODE3 dimensionsconservative

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Definition

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

Properties

Lyapunov spectrum

$+0.001792,\; -0.008737,\; -0.01545$
computed at build

Kaplan–Yorke dimension

$D_{KY} = 1.205$

Divergence ∇·f

$\nabla\!\cdot f = y_{2}$
state-dependent

Equilibria

none found (no equilibria)

Define it in TSDynamics

import tsdynamics as ts

sys = ts.systems.SprottA()
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{sprotta,
  title = {SprottA system},
  note = {Sprott (1994), Phys. Rev. E 50, R647-R650}
}