Bifurcation And Chaotic State In Forced Oscillatory Circuits Containing Saturable Inductors

Bifurcations of periodic, quasi-periodic and chaotic oscillations are most frequently observed in forced nonlinear circuits containing saturable inductors, whose dynamics are described by nonautonomous dierential equations with periodic external forcing terms. A Poincare mapping is commonly applied to the study of the bifurcation phenomena. We present some elementary discussion of the codimension one and two bifurcations of periodic solution and give a practical method to obtain various bifurcation diagrams. As illustrated examples, we show numerical results for typical circuits. 1 Introduction: Circuit Model and its Dynamics An electric circuit containing a saturable inductor exhibits various nonlinear phenomena 1 , such as the coexistence of several periodic oscillations which are correlated with the jump and hysteresis behaviors, the fundamental, higher-harmonic and sub-harmonic resonances, the appearance of quasi-periodic and chaotic states of oscillations, etc. The state chang..