SprottM¶

Systems / ODEs / Chaotic attractors

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

continuous · ODE3 dimensionschaotic

Interactive: drag to rotate

Definition¶

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

Parameters¶

Symbol	Default	Role
`a`	`1.7`	adjustable coefficient

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