Bifurcation of nonlinear circuits with periodically operating switch

This paper considers the Alpazur oscillator, which is composed of a Rayleig h oscillator unit and a de power supply controlled by a switch, and examine s the bifurcation set by numerical calculation. In such a case, a bifurcati on diagram is constructed in order to see the phase-space behavior of the s ystem. In the conventional method, however, the calculation is possible onl y when the trajectory is continuous and differentiable. The method cannot d irectly be applied to the case where the trajectory is discontinuous or not smooth at a point (not differentiable) as in the case of on-off circuits. From such a viewpoint, this paper proposes a bifurcation trajectory trackin g algorithm for the that nonlinear on-off circuit, containing a switch that is made on and off periodically by an external force. As the method of ana lysis, the composite Poincare mapping is defined based on the periodic oper ation of the switch. The method of calculating the bifurcation parameter is described precisely. Using the proposed method, the Alpazur oscillator is analyzed. The phase-synchronized solutions that exist along the Neimark-Sac ker bifurcation as well as the chaos are investigated. (C) 2000 Scripta Tec hnica.