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中文核心期刊

全局分析的广义胞映射图论方法

GENERALIZED CELL MAPPING DIGRAPH METHOD FORGLOBAL ANALYSIS

  • 摘要: 应用广义胞映射理论的离散连续状态空间为胞状态空间的基本概念,依循Hsu的将偏序集和图论理论引入广义胞映射的思想,以集论和图论理论为基础,提出了进行非线性动力系统全局分析的广义胞映射图论方法.在胞状态空间上,定义二元关系,建立了广义胞映射动力系统与图的对应关系,给出了自循环胞集和永久自循环胞集存在判别定理的证明,这样可借助国论的理论和算法来确定动力系统的全局性质.应用图的压缩方法,对所有的自循环胞集压缩后,在全局瞬态分析计算中瞬态胞的总数目得到有效地减少,并能借助于图的算法有效地实现全局瞬态的拓扑排序.在整个定性性质的分析计算中,仅采用布尔运算.

     

    Abstract: In this paper, according to Hsu's idea that posets and digraphs are introduced intogeneralized cell mapping, a generalized cell mapping digraph method is presented by using thetheory of generalized cell mapping discretizing the continuous state space into the cell state spaceand the theories of set and digraph to achieve the task of global analysis of nonlinear dynamicalsystems. In the cell state space, we make the correspondence between generalized cell mappingdynamical systems and digraphs. The demonstrat...

     

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