Mechanism for taming chaos by weak harmonic perturbations

Taming chaos by weak harmonic perturbations has been a hot topic in recent years. This paper is the first report which clarifies the mechanism for taming chaos theoretically. The model we consider in this paper is a forced Raleigh oscillator with a diode. To simplify analyses, we consider the degenerate case where the diode 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 bifurcation.