CHUA ELECTRICAL CIRCUIT

The dynamical system

where

represents a mathematical model of an LRC circuit consisting of a linear resistance, two linear capacitances, a linear inductance and a non-linear diode. The parameters of the system satisfy , .

There are three equilibrium points

The characteristic polynomial for the equilibrium point at the origin is

Thus and hence the equilibrium point is unstable.

The characeristic polynomials for the two equilibria are identical and given by

There is a bifurcation at

where the equilibrium point changes from unstable to stable as becomes greater than the bifurcation value.

Maple Analysis

SIMULATION

Taking parameter values the critical value of . The plots below show the behaviour of the system as is decreased.

Pair of Limit Cycles

Period Doubling

Two Strange Attractors

The Double Scroll Attractor

The link below provides a Java simulation of the system.

Java Simulation

Parameter values and initial conditions can be changed.

An alternative series of simulations is available using Maple.

Maple Simulation