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分段线性电路切换系统的复杂行为及非光滑分岔机理*
Complicated behaviors and non-smooth bifurcation of a switching system with piecewise linear chaotic circuit*
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摘要: 分析了分段线性电路系统在周期切换下的复杂动力学行为及其产生的机理.基于平衡点分析,给出了两子系统Fold分岔和Hopf分岔条件.考虑了在不同稳定态时两子系统周期切换的分岔特性,产生了不同的周期振荡,并揭示了其产生的机理.在不同的周期振荡中,切换点的数量随参数变化产生倍化,导致切换系统由倍周期分岔进入混沌.Abstract: The complex dynamical and non-smooth bifurcations of a compound system with periodic switches between two piecewise linear chaotic circuits are investigated. Based on the analysis of equilibrium states, the conditions for Fold bifurcation and Hopf bifurcation are derived to explore the bifurcations of the compound system with periodic switches while there are different stable solutions in the two subsystems. Different types of oscillations of the swithing system are observed, and the mechanism is studied and presented. In the difference of periodic oscillations, the number of the swithing points increases doubly with the variation of the parameter, which leads from period-doubling bifurcation to chaos.
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