Cluster Synchronization In Complex Networks

This thesis focuses on the cluster synchronization in complex networks,and cluster synchronization of variable and fixed clusters in networks is studied.About cluster synchronization of variable clusters,we first study cluster synchronization on single-layer network with different topological structures.Due to interaction between nodes,different topological structures will lead to different cluster synchronization phenomena.Multi-layer networks that interact with each other are ubiquitous in the real world.We further consider cluster synchronization in the original network layer(we call it the interested layer)under the influence of other networks(we call it the influencing layer).Results show that cluster synchronizability of the interested layer is closely related to the topological structure of the influencing layer.We further discuss the impact of the density and community module of the influencing layer.In addition,different connection patterns between the influencing layer and the interested layer will also affect cluster synchronization on the interested layer.The connection patterns include positive correlation,negative correlation and random correlation.About cluster synchronization of fixed clusters,we extend the undirected network to a bidirectional network and take it as the research object.The coupling strengths of the directed edges in the bidirectional network are determined only by the nodes,and they are equal if the corresponding directed edges are from the same node.All nodes in the network are divided into some clusters in advance.With the constructed controller and adaptive coupling,cluster synchronization can be realized in the network.