SprottK¶

Systems / ODEs / Chaotic attractors

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

continuous · ODE3 dimensionschaotic

Interactive: drag to rotate

Definition¶

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

Parameters¶

Symbol	Default	Role
`a`	`0.3`	adjustable coefficient

Properties¶

Lyapunov spectrum

$+0.02135,\; +0.02251,\; -0.8964$
computed at build

Kaplan–Yorke dimension

$D_{KY} = 2.049$

Divergence ∇·f

$\nabla\!\cdot f = a + y_{1} - 1$
state-dependent

Equilibria

1 equilibria
0 stable · 1 unstable

Define it in TSDynamics¶

import tsdynamics as ts

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