耦合动力系统的Conley指标  

Conley index for coupled dynamical systems

作　　者：谭定富[1] 王凯华[2] 傅新楚[1] 

机构地区：[1]上海大学理学院,上海200444 [2]海南师范大学数学与统计学院,海口571127

出　　处：《应用数学与计算数学学报》2012年第4期382-395,共14页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金资助项目(11072136)

摘　　要：从Hessian矩阵入手,研究了几种有限网络上动力系统的两种孤立不变集的Conley指标.对于网络节点仅具有单个状态参量时,分析了在线性耦合关系和非线性耦合关系下的全连接网络(全耦合网络)、最近邻网络和任意连接网络上流的孤立不动点的Conley指标与单个节点状态流的孤立不动点的Conley指标的关系;对于节点具有双状态参量和孤立节点不变集为极限环时,给出了在一定耦合条件下,文中所定义的映射F(s)的C0nley指标与节点状态积流的Conley指标的关系.The Conley indices for two kinds of isolated invariant sets of several finite network systems are discussed. For nodes with a single state parameter, the relationship between the Conley indices for an isolated fixed point of a flow on an isolated node and for that on a network is analyzed. For nodes with double state parameters and an invariant set consisting of a limit cycle, the relationship between the Conley indices for a product flow of nodes and for the map which is defined is analyzed under certain coupling conditions.

关 键 词：CONLEY指标 HESSIAN矩阵 复杂网络 不动点 极限环 

分 类 号：O19[理学—数学] O175[理学—基础数学]