Bifurcation and Chaotic State in Forced Oscillatory Circuits Containing Saturable Inductors *

Abstract

Bifurcations of periodic, quasi-periodic and chaotic oscillations are frequently observed in forced nonlinear circuits described by nonautonomous differential equations with a periodic external forcing term. Qualitative analysis using the Poincaré mapping is commonly applied in the study of bifurcation phenomena as well as in numerical analysis of periodic and non-periodic solutions. The purpose of this paper is to present some elementary mechanisms of the bifurcations, and to discuss numerical methods for analyzing these nonlinear phenomena. As illustrated examples, numerical results of forced oscillatory circuits containing saturable inductors are presented.