Complicated behaviors as well as the mechanism of the switching circuit

Abstract

Switching electrical circuit with switcher between different types of Jerk systems is established. Based upon the analysis of equilibrium states, stable focus as well as periodic oscillations via Hopf bifurcation can be observed in the two subsystems as parameters varies. Complicated behavior caused by the periodic switcher is investigated in detail, and the point/circle and circle/circle switching periodic oscillations as well as the mechanism are presented. In the different types of switching oscillations, the number of the switching points on the trajectory may increase doubly with the variation of the parameter, which may lead to the cascade of period-doubling bifurcation to chaos. Furthermore, the variation of the parameter may influence the amplitude of the periodic oscillation of the subsystem and therefore the structure of the attractor of the whole switching system.