EI、Scopus 收录
中文核心期刊

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

  • 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.

     

    Abstract: Digraph cell mapping method (DCMM) is an effectivetechnique to analyze the global behavior of dynamical systems. Recently, ithas been applied to the study of crises and stochastic bifurcation, whichachieved a series of good results. However, many researches by DCMM arebased on smooth dynamical systems, and it is unknown whether this method canbe applied to non-smooth systems. In this paper, the key problem namedexpansion of cell flow is discussed in detail when the digraph cell mappingmethod is applied to analyze non-smooth dynamical systems. It is found thatbecause of non-smooth boundary the expansion of cell flow is usuallyserious, which may result in analysis distortion of DCMM. For the aboveproblem, the notion of the artificial node set is introduced to record whichstate cells may cause the expansion of cell flow. Taking the artificial nodeset as the redivided object, an iterative version of DCMM together with itseffective algorithm is designed to decrease the expansion of cell flow andimprove the computing accuracy. Furthermore some remarks are suggested forreaders to analyze complex non-smooth systems. In the iterative processes,the present method can not only keep the integrality of all computingresults but also significantly enhance the computing efficiency. As anillustrative example, the Duffing-van der Pol vibro-impact system withcomplex nonlinear structures is taken to demonstrate the validity of theproposed method.

     

/

返回文章
返回