Abstract
By introducing the periodic parameter-switching scheme to the Lorenz oscillator, a switched dynamic model is established. In order to investigate the mechanism of the behaviors of the switched system, the Poincare map of the whole system is defined by suitable local sections and local maps. Different types of periodic oscillations and their transitions to chaos in the system can be observed. Based on the conditions when the Floquet multiplies of corresponding fixed point associated with the periodic solution pass the unit circle, some bifurcation curves are obtained in the plane of bifurcation parameters, dividing the parameters plane into several regions corresponding to different kinds of oscillations. Meanwhile, bifurcation scenarios, such as fold bifurcation, pitchfork bifurcation and period-doubling bifurcation, are determined in the switched system.
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