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一类多尺度变量动力学系统中多环同宿轨分岔问题研究

发表时间:2010-02-15  浏览量:1711  下载量:585
全部作者: 岳宝增
作者单位: 北京理工大学宇航学院
摘 要: 对一类多尺度变量耦合动力学系统多环同宿轨分岔问题进行深入的数值探索和研究。通过对全局分岔图的分析,揭示了自我复制系统动力学特性与参数空间中折叠分岔的层次结构密切相关。数值结果表明:Bogdanov�Takens分岔点以及对应于某一同宿轨的角状形参数域对系统的周期轨、同宿轨全局分岔以及复杂混沌动力学具有决定性作用。数值仿真过程揭示了反应扩散系统中调制的二脉冲及多脉冲解的存在并伴随有脉冲自我复制及分裂过程。
关 键 词: 动力学与控制;全局分岔;模式;同宿环;脉冲;层次结构
Title: Study on bifurcation of multi�pulses homoclinic orbits in a system containing multi�scale variables
Author: YUE Baozeng
Organization: School of Astronautical Engineering, Beijing Institute of Technology
Abstract: The paper studied an extensive numerical exporation of delicate global dynamics of the multi�pulses homoclinic orbits in an one kind of dyanamic system containing multi�scale variables. A careful analyisis of the scenario of the global fifuircation diagram suggests that the dynamics of self�repliating system is related to a hierarchy structure of dolding bifurcation branches in parameter regions. The numerics suggests the Bogdanov�Takens points together with a presence of a horn of parameter values emanates from the particular codim 2 homoclinic orbit play a central role for global bifrcatiion of periodic orbits and the homoclinic solutions and the complex chaotic dynamics. Numerical simulation also reveals the existence of the mkulating two�pulses or multi�pulse, which companying the procedure of puilse self�rplicaing and splitting in reation�diffusion systems.
Key words: dynamics and control; global bifurcation; patterns; homoclinic orbits; pulses; hierarchy structure
发表期数: 2010年2月第3期
引用格式: 岳宝增. 一类多尺度变量动力学系统中多环同宿轨分岔问题研究[J]. 中国科技论文在线精品论文,2010,3(3):265-272.
 
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