SprottDelay¶

Systems / DDEs / Delayed systems

A minimal scalar delay equation engineered for chaos from one nonlinear term.

delay · DDE1 dimensionchaotic

Interactive: drag to rotate

Definition¶

\[ \begin{aligned} \dot{x} &= \sin{\left(x{\left(t - \tau \right)} \right)} \end{aligned} \]

Parameters¶

Symbol	Default	Role
`tau`	`5.1`	feedback delay

State variables: x

Properties¶

Lyapunov spectrum

TODO — DDE Lyapunov not computed at build time

Kaplan–Yorke dimension

TODO — requires a numeric Lyapunov spectrum

Divergence ∇·f

$\nabla\!\cdot f = 0$
constant

Equilibria

TODO — fixed_points failed: NotImplementedError

Use it in TSDynamics¶

import tsdynamics as ts

system = ts.systems.SprottDelay()
traj = system.run(final_time=500.0, dt=0.5)
ts.plot(traj)

# DDE Lyapunov uses the infinite-dimensional-history estimator:
spectrum = ts.analysis.lyapunov_spectrum(system, k=1, dt=0.5, ic=traj.y[-1])

Reference¶

Sprott (2007), Physics Letters A 366, 397-402
doi:10.1016/j.physleta.2007.01.083

BibTeX

@misc{sprottdelay,
  title = {SprottDelay system},
  note = {Sprott (2007), Physics Letters A 366, 397-402},
  doi = {10.1016/j.physleta.2007.01.083}
}