Mechanism for taming chaos by weak harmonic perturbations

Taming chaos by weak harmonic perturbations has been a hot topic in recent years. This paper clarifies the mechanism for taming chaos theoretically. T he model we consider in this paper is a forced Rayleigh oscillator with a d iode. To simplify analyses, we consider the degenerate case, where the diod e in the circuit operates as a switch. In this case, the governing equation of the circuit is represented by a constrained equation, and the Poincare map is derived rigorously as a one-dimensional map. By the analysis of the Poincare map, we clarify that taming chaos occurs by a saddle-node bifurcat ion.