标题： 耦合非相同动力学系统的网络中的聚类同步 显示英文标题

标题： Cluster synchronization in networks of coupled non-identical dynamical systems

摘要： 在本文中，我们研究耦合非相同动力系统网络中的聚类同步。 同一聚类中的顶点具有相同的无耦合节点系统的动力学，但不同聚类中的无耦合节点系统是不同的。 我们提出了保证聚类同步的条件，并研究了聚类同步与无权图拓扑之间的关系。 我们指出两个条件在聚类同步中起关键作用：共同的跨聚类耦合条件和聚类内通信。 从后者出发，我们通过通信路径的边是否位于跨聚类或聚类内来解释两种著名的聚类同步方案：自组织和驱动。 通过这种方式，我们根据如果想要保持同一聚类中顶点对之间的通信，跨聚类边或聚类内边的集合是否可移除来对聚类进行分类。 此外，我们提出了对底层图权重的自适应反馈算法，这些算法可以同步满足上述两个条件的任何双向网络。 我们还给出了几个数值例子来说明理论结果。 显示英文摘要

摘要： In this paper, we study cluster synchronization in networks of coupled non-identical dynamical systems. The vertices in the same cluster have the same dynamics of uncoupled node system but the uncoupled node systems in different clusters are different. We present conditions guaranteeing cluster synchronization and investigate the relation between cluster synchronization and the unweighted graph topology. We indicate that two condition play key roles for cluster synchronization: the common inter-cluster coupling condition and the intra-cluster communication. From the latter one, we interpret the two well-known cluster synchronization schemes: self-organization and driving, by whether the edges of communication paths lie at inter or intra-cluster. By this way, we classify clusters according to whether the set of edges inter- or intra-cluster edges are removable if wanting to keep the communication between pairs of vertices in the same cluster. Also, we propose adaptive feedback algorithms on the weights of the underlying graph, which can synchronize any bi-directed networks satisfying the two conditions above. We also give several numerical examples to illustrate the theoretical results.