非线性切换系统的复杂行为及其机理分析

项目名称： 非线性切换系统的复杂行为及其机理分析

项目编号： No.11472115

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 毕勤胜

作者单位： 江苏大学

项目金额： 86万元

中文摘要： 作为一类典型的混杂系统，非线性切换系统具有广泛的工程背景，其复杂动力学行为及其机理研究是当前国内外动力学与控制领域的热点课题之一。本项目围绕非线性切换系统，考察具有不同特性的光滑子系统，尤其是在自治系统和周期激励系统之间的切换导致的各种动力学行为，通过分析子系统的各种平衡态及其分岔以及切换点的动力特性，探讨不同行为的产生原因，着重考察在具有不同特性的子系统及各种切换模式，特别是在诸如多平衡态参与切换，子系统存在高余为分岔、切换点处于临界位置以及存在各种共振关系等情形下切换系统的动力学特性，探讨各种因素诸如参数变化、子系统的分岔、切换模式的微扰等等对切换系统动力学演化过程的影响，研究不同切换模式所引起的系统行为差别及其产生原因，揭示切换系统的各种动力学行为及其产生机制，为发展非线性切换系统理论及实际工程应用提供服务。

中文关键词： 非线性动力系统；复杂行为；高余维分岔；分岔机理；稳定性

英文摘要： As a class of typical hybrid system, nonlinear swtiched system has wide engineering background, the complicated dynamical behaviors as well as the mechanism of which 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 to investigate different types of dynamical behaviors caused by the switching between smooth subsystems with different characteristics,especially between autonomous system and periodically excited system. Based on the analysis of the steady states as well as the bifurcations of the subsystems, the mechanism of different behaviors will be explored. Specificially, the dynamics of the switched systems will be discussed with different conditions such as the cases for subsystems with different characteristics and different switching forms, especially for the cases with different steady states involving in the behaviors, high codimensional bifurcations in the subsystems, the swithing point located at the critical position and different forms of internal resonance.The influence of the factors such as the variation of the parameters, the bifurcations in the subsystems, the small disturbance of the switching on the dynamical evolution of the switched system will be investigated.The difference of the behaviors as well as the mechanism caused by different forms of switching will be discussed to explore the dynamics as well as the mechanism of the switched system. The results obtained may serve for the advancement of the theory of nonlinear switched system as well as the practical enginneering applications.

英文关键词： Nonlinear dynamical systems;Complicated behavior;High co-dimensional bifurcation;Bifurcation mechanism;Stability