JerkCircuit

Systems / ODEs / Physical systems

A minimal third-order 'jerk' circuit — chaos from one nonlinear element.

continuous · ODE3 dimensionschaoticcircuit

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Definition

\[ \begin{aligned} \dot{y_{0}} &= y_{1} \\ \dot{y_{1}} &= y_{2} \\ \dot{y_{2}} &= - eps \left(e^{\frac{y_{1}}{y_{0}}} - 1\right) - y_{0} - y_{2} \end{aligned} \]

Parameters

Symbol	Default	Role
eps	1e-09	diode saturation-current scale (nonlinearity strength)
y0	0.026	diode thermal-voltage scale (exponential steepness)

Properties

Lyapunov spectrum

$+0.007788,\; -0.02918,\; -0.9786$
computed at build

Kaplan–Yorke dimension

$D_{KY} = 1.267$

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.JerkCircuit()
traj = sys.integrate(final_time=100.0, dt=0.01)

exps = sys.lyapunov_spectrum()
ts.kaplan_yorke_dimension(exps)

Reference

Sprott (2011), IEEE Trans. Circuits Syst. II 58, 240-243

BibTeX

@misc{jerkcircuit,
  title = {JerkCircuit system},
  note = {Sprott (2011), IEEE Trans. Circuits Syst. II 58, 240-243}
}