Cluster Synchronization of Delayed Complex Dynamical Networks With the Intracluster and Intercluster Link Dynamics

ABSTRACT This paper focuses on investigating the cluster synchronization (CS) of delayed complex dynamical networks (CDNs) with both intracluster and intercluster link dynamics. According to the similar properties of nodes, such as state dimensions and network latency, the node dynamics of each cluster in the network is first modeled. Based on the large‐scale system theory, we then propose a novel model of CDNs composed of the three interconnected dynamics: the node dynamics, the intracluster link dynamics and intercluster link dynamics. The CS happens in each cluster, which means that the state errors converge to zero. However, the link dynamics of both intracluster and intercluster are ignored in the existing literature about the CS. In view of this, by using the coupling mechanisms in the link dynamics of intracluster and intercluster and synthesizing the control scheme, the CS of the novel delayed CDNs is asymptotically achieved. The results in this paper show that the CS happens when the two link dynamics can track, respectively, the synthesized auxiliary dynamic tracking targets. Finally, a CDN consisting of various interconnected systems is applied to verify the effectiveness of our proposed method.