Bifurcation analysis of Lu system with the periodic parameter-switching scheme

In this paper, switches related to the parameters altered periodically are introduced, upon which a typical switched dynamical model between two Lu systems is established. To explore the dynamical behaviors and the mechanism of the switching oscillations, Poincare´ map of the whole system is defined by the switching conditions and piecewise maps. The location of the fixed points corresponding to various periodic switching oscillations and associated Floquet multipliers are calculated, based on which bifurcation scenarios, such as saddle-note bifurcation, pitchfork bifurcation and period-doubling bifurcation, are determined in the switched Lu system.