Oscillations and non-smooth bifurcation analysis of Chen system with periodic switches

Abstract

Complicated behaviors of a compound system with periodic switches between different types of Chen systems are investigated in detail. In the local analysis, the critical conditions such as fold bifurcation and Hopf bifurcation are derived to explore the bifurcations of the compound systems with different stable solutions in the two subsystems. Different types of oscillations of this switched system are observed, of which the mechanism is presented to show that the trajectories of the oscillations can be divided into several parts by the switching points, governed by the two subsystems respectively. Because of the non-smooth characteristics at the switching points, different forms of bifurcations may occur in the compound system, which may result in complicated dynamics such as chaotic oscillations, instead of the simple connections between the trajectories of the two subsystems. By the Poincaré mapping, the location of the fixed point and Floquet characteristic multiplier of switching system are discussed.With the variation of the parameter, the system can evolve into chaos via the cascading of period-doubling bifurcation. Besides, the system can evolve into chaos immediately by saddle-node bifurcations from period solutions.The non-smooth bifurcation mechanism of periodic switching system can be revealed by the research.