Sinusoidal excitation on the Chua's circuit simulation of limit cycles and chaos

Abstract

Experiments with modelling and simulation of sinusoidal excitation on Chua's circuit are presented. It is demonstrated that the behaviour of the circuit is based on the interaction of two different kinds of energy balance: chaotic behaviour based on a balance between two unstable “states of charging”, and stable limit cycle behaviour based on the balance between the energy lost in the regions with mainly positive losses and the energy gained in the regions with mainly negative losses. Convergence problems observed in connection with simulation of the ideal piecewise-linear model are solved by means of a smooth continuous model of the nonlinear element based on the ideal operational amplifier model instead of a polynomial approximation. The movements of the eigenvalues as functions of the nonlinear resistance are found. Stable limit cycles of periods 1, 2, 3 and 5 are found by introducing losse