三类切换模式下的非线性振荡行为及其机理

作为一类典型的混杂系统，切换系统具有广泛的工程背景，其在不同切换模式下产生的复杂动力学行为及其机理研究是当前国内外动力学领域的热点课题之一。本项目围绕时间、状态以及两者混合切换模式下的非线性切换系统，考察具有不同特性的子系统在此三类切换模式下来回切换导致的各种动力学行及其机理。通过将整个系统离散化，给出整个系统各种切换行为尤其是周期切换振荡；分析子系统各平衡态及其相应的分岔模式，探讨子系统行为在不同切换模式连接下的动态特性的区别，揭示不同切换振荡的特征及其相应的机理；同时分析整个系统随子系统参数，切换模式参数变化的动力学演化过程，进而揭示不同切换模式下各种切换振荡相应的分岔机制，探索整个系统通往复杂性运动的道路。本项目为发展非线性切换系统理论及实际工程应用提供服务。

As a class of typical hybrid system, nonlinear switched system has wide engineering background, the complicated dynamical behaviors as well as the mechanism of which with different switching modes become a key problem in the research area of dynamical and control at home and abroad. In the project, we will focus on the nonlinear switched system associated with time, state and mixed switching modes to investigate different types of dynamical behaviors caused by the three switching modes between subsystems with different characteristics. Based on the discrete system defined by the switching modes and the solutions of the subsystems, the different switching oscillations will be obtained, especially the periodic switching oscillations. By the analysis of the steady states as well as the bifurcations of the subsystems, the difference of the dynamical behaviors caused by the three switching modes will be explored, and the mechanism of switching oscillations will be discussed in detail. The dynamical evolutions with the variations of the subsystem parameters and the parameters in switching modes will be analyzed and the different types of bifurcations of the periodic switching oscillation will be presented to explore the mechanism of the complexity. The results obtained may serve for the advancement of the theory of nonlinear switched system as well as the practical engineering applications.