JerkCircuit

Systems / ODEs / Physical systems

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

continuous · ODE3 dimensionschaoticcircuit

Interactive: drag to rotate

Definition

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

Parameters

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

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

1 equilibria
0 stable · 1 unstable

Use it in TSDynamics

import tsdynamics as ts

system = ts.systems.JerkCircuit()
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 (2011), IEEE Trans. Circuits Syst. II 58, 240-243
doi:10.1109/tcsii.2011.2124490

BibTeX

@misc{jerkcircuit,
  title = {JerkCircuit system},
  note = {Sprott (2011), IEEE Trans. Circuits Syst. II 58, 240-243},
  doi = {10.1109/tcsii.2011.2124490}
}