非线性切换系统的动力学行为分析

建立了周期切换下的非线性电路模型，基于子系统平衡点及其稳定性分析，分别给出了其相应的fold分岔和Hopf分岔条件，讨论了子系统在不同平衡态下由周期切换导致的各种复杂行为，指出切换系统的周期解随参数的变化存在着倍周期分岔和鞍结分岔两种失稳情形，并相应地导致不同的混沌振荡，进而结合系统轨迹及其相应的分岔分析，揭示了各种振荡模式的动力学机理. 关键词： 周期切换 倍周期分岔 鞍结分岔 混沌

Analysis of dynamical behaviors in a nonlinear switching circuit system

A nonlinear circuit model with periodic switching is established. The fold bifurcation and Hopf bifurcation sets of the subsystems are derived via the analysis of the relevant equilibrium points as well as the stabilities. Complex dynamical behaviors caused by periodic switching in various equilibrium states of subsystems are investigated. The results show that there exist two types of destabilizing cases, i.e., period-doubling bifurcation and saddle-node bifurcation, in the variation of periodic solution to the switching system with parameter, leading to different forms of chaotic oscillations correspondingly. Furthermore, by analyzing the the phase trajectory and its corresponding bifurcation, the mechanisms for different types of oscillations are presented, which can explain some phenomena of the switched dynamical system.
Keywords： periodic switching period-doubling bifurcation saddle-node bifurcation chaos