非光滑连续系统的簇发振荡模式及其分岔机理研究

项目名称： 非光滑连续系统的簇发振荡模式及其分岔机理研究

项目编号： No.11302086

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 季颖

作者单位： 江苏大学

项目金额： 26万元

中文摘要： 实际系统中广泛存在的各种非光滑因素引起了人们的高度关注，已成为当前非线性动力学研究的热点和难点之一。本项目拟围绕非光滑连续系统，考虑其中各状态量变化速率间的差异，基于非光滑分岔理论，分自治和非自治两种情形探究系统的各种非光滑簇发振荡模式及其诱发机制。在自治条件下，分析快子系统在不同运动状态转迁过程中所涉及的不同吸引子的非光滑分岔，着重关注向量场不同分界面引起的平衡点非光滑分岔之间的相互作用以及极限环的余维二分岔，给出自治非光滑连续系统多种簇发振荡模式的分岔转迁机制及其拓扑类型；在非自治条件下，主要探讨周期激励调制下系统经由滞后环的簇发振荡。分析周期激励导致滞后环产生的非光滑分岔机制和类型，进而探讨快子系统在静息态和激发态之间转迁的非光滑分岔模式，揭示系统经由不同类型滞后环的多种簇发振荡模式以及周期激励形式对簇发振荡行为的影响。上述研究将为非光滑系统理论发展和工程应用提供服务。

中文关键词： 非光滑连续系统；簇发振荡；向量场分界面；非光滑分岔；周期刺激

英文摘要： As the non-smooth dynamical systems are becoming more and more important in engineering fields, they draw attention of many scientific workers and engineers. The non-smooth dynamical systems have been one of the hot spot of nonlinear dynamics study in recent years. This subject will study the bursting behavior and the associated induced mechanisms in non-smooth continuous systems based on non-smooth bifurcation analysis. Its main contents are presented as follows: In the autonomous case, bursting of point-point type and bursting of point-cycle type will be investigated in this subject. The bifurcation of a rest state leading to repetitive spiking (the bifurcation for the emergence of a spiking state) and the bifurcation of a repetitive spiking state leading to the rest state (the bifurcation for the termination of a spiking state) will be explored to distinguish the topological classification of bursting behaviors. Especially, there will be an analysis of the interaction between the bifurcations of equilibria at different switching boundaries as well as the co-dimension two bifurcation of limit cycle. In the non-autonomous case, the dynamics of system with periodic excitation will be discussed. Concretely, the periodic excitation is taken as the bifurcation parameter of fast subsystem. Non-smooth bifurcations b

英文关键词： non-smooth continuous systems；bursting；switching boundaries；non-smooth bifurcation；periodic stimulation