项目名称： 高余维分岔下的簇发振荡及其机理分析

项目编号： No.11472116

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： 张正娣

作者单位： 江苏大学

项目金额： 75万元

中文摘要： 不同尺度耦合系统具有广泛的工程背景，深入分析高余维下的簇发振荡及其机理具有重要的理论意义及潜在的应用价值，也是当前国内外非线性研究的热点和前沿课题之一。本项目围绕多尺度耦合非线性动力系统，通过分离快慢子系统，深入分析不同尺度上子系统的各种平衡态及其分岔行为，尤其是高余维分岔模式。探讨不同沉寂态和激发态失稳条件，结合慢子系统的各种调节行为，考察各种条件下簇发振荡的动力特性及其相应的分岔机理，探讨不同耦合方式及参数对耦合系统演化过程的影响规律，结合各种分岔的标准型，给出开折参数下所有可能的微扰特征，揭示不同簇发尤其是高余维分岔连接快慢时的簇发行为的特征及其相应的机理，进而研究不同周期激励模式下两时间尺度耦合系统的各种簇发行为及其分岔机制，探讨不同分岔下的簇发振荡的本质，给出不同簇发振荡的标准型，并进一步将结果推广到分析三时间尺度耦合系统的簇发，为发展多时间尺度耦合系统理论提供支撑。

中文关键词： 非线性动力学；簇发振荡；高余维分岔；分岔机理；稳定性

英文摘要： On the fact that the wide engineering background of the coupled system with multiple time scales, further investigation of the bursting oscillations as well as the associated mechanism with high codimension not only has important theoretical and potential applied significaance, but also is one of the key problems in the study of nonlinear dynamics at home and abroad.In this project,we focus on the nonlear dynamics with multiple time scales, and explore the steady states as well as the bifurcations of the subsystems on different scales, especially the bifurcation forms with high codimension. The dynamics of the bursting oscillation as well as the related bifurcation mechanism with different conditions will be investigated, while the influence of the coupling forms as well as the parameters on the evolution of the dynamical behaviors will be discussed. The characteristics of different bursting oscillations as well as the mechanism,especially for those with high codimension bifurcations will be revealled. Furthermore, the bursting oscillation as well as the mechanism with different forms of periodic excitation will be discussed to explore the bursting oscillation with different bifurcations as well as the normal forms and finally, all the results may be extended to the coupled system with three time scales, which may serve for the advancement of the theory of couled dynamical systems with multiple time scales.

英文关键词： Nonlinear Dynamical systems;Bursting oscillation;High co-dimensional bifurcation;Bifurcation mechanism;Stability