非光滑动力系统的迭代图胞映射法  

THE ITERATIVE DIGRAPH CELL MAPPING METHOD OF NON-SMOOTH DYNAMICAL SYSTEMS

作　　者：李爽[1] 贺群[2] 

机构地区：[1]西安财经学院统计学院,西安710100 [2]武警工程学院基础部数学教研室,西安710086

出　　处：《力学学报》2011年第3期579-585,共7页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金(10802061);陕西省教育厅基金(09JK438);西安统计研究院基金(09JD06)资助项目~~

摘　　要：分析了图胞映射方法在处理非光滑动力系统过程中遇到的关键问题——胞流扩张.为了有效减小胞流扩张,基于迭代图胞映射方法,通过引入人工顶点集的概念,构建了非光滑系统迭代图胞映射具体实施方案,讨论了在此过程中值得注意的事项.结合典型实例分析,证实了该方法的有效性.Digraph cell mapping method（DCMM） is an effective technique to analyze the global behavior of dynamical systems.Recently,it has been applied to the study of crises and stochastic bifurcation,which achieved a series of good results.However,many researches by DCMM are based on smooth dynamical systems, and it is unknown whether this method can be applied to non-smooth systems.In this paper,the key problem named expansion of cell flow is discussed in detail when the digraph cell mapping method is applied to analyze non-smooth dynamical systems.It is found that because of non-smooth boundary the expansion of cell flow is usually serious,which may result in analysis distortion of DCMM.For the above problem,the notion of the artificial node set is introduced to record which state cells may cause the expansion of cell flow.Taking the artificial node set as the redivided object,an iterative version of DCMM together with its effective algorithm is designed to decrease the expansion of cell flow and improve the computing accuracy.Furthermore some remarks are suggested for readers to analyze complex non-smooth systems.In the iterative processes,the present method can not only keep the integrality of all computing results but also significantly enhance the computing efficiency. As an illustrative example,the Duffing-van der Pol vibro-impact system with complex nonlinear structures is taken to demonstrate the validity of the proposed method.

关 键 词：迭代图胞映射方法 非光滑 全局分析 吸引子 混沌鞍 

分 类 号：O322[理学—一般力学与力学基础]