SprottI¶

Systems / ODEs / Chaotic attractors

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

continuous · ODE3 dimensionschaotic

Interactive: drag to rotate

Definition¶

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

Parameters¶

Symbol	Default	Role
`a`	`0.2`	adjustable coefficient

Properties¶

Lyapunov spectrum

$+0.0105,\; -0.007556,\; -1.003$
computed at build

Kaplan–Yorke dimension

$D_{KY} = 2.003$

Divergence ∇·f

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

Equilibria

1 equilibria
0 stable · 1 unstable

Define it in TSDynamics¶

import tsdynamics as ts

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