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

Interactive: drag to rotate

Definition

\[ \begin{aligned} \dot{x} &= y \\ \dot{y} &= - x + y z \\ \dot{z} &= 1 - y^{2} \end{aligned} \]

Properties

Lyapunov spectrum

TODO — lyapunov_spectrum failed: AttributeError

Kaplan–Yorke dimension

TODO — requires a numeric Lyapunov spectrum

Divergence ∇·f

$\nabla\!\cdot f = z$
state-dependent

Equilibria

none found (no equilibria)

Use it in TSDynamics

import tsdynamics as ts

system = ts.systems.SprottA()
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

Sprott (1994), Phys. Rev. E 50, R647-R650
doi:10.1103/physreve.50.r647

BibTeX

@misc{sprotta,
  title = {SprottA system},
  note = {Sprott (1994), Phys. Rev. E 50, R647-R650},
  doi = {10.1103/physreve.50.r647}
}