中文摘要：

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Conley指标与节点状态积流的Conley指标的关系.

英文摘要：

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.