Bifurcation of nonlinear circuits with periodically operating switch

Abstract

This paper considers the Alpazur oscillator, which is composed of a Rayleigh oscillator unit and a dc power supply controlled by a switch, and examines the bifurcation set by numerical calculation. In such a case, a bifurcation diagram is constructed in order to see the phase-space behavior of the system. In the conventional method, however, the calculation is possible only when the trajectory is continuous and differentiable. The method cannot directly 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 tracking 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 analysis, the composite Poincaré mapping is defined based on the periodic operation 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–Sacker bifurcation as well as the chaos are investigated. © 2000 Scripta Technica, Electron Comm Jpn Pt 3, 84(1): 75–83, 2001