Cluster Synchronization in a Heterogeneous Network with Mixed Coupling via Event-Triggered and Optimizing Pinning control

This work presents a unique model that includes both generic linear systems and nonlinear oscillators coupled to each other. Information exchange among nonidentical nodes is orchestrated by a directed network topology with cooperative-competitive interactions. The communication occurs not only within the nodes belong to the same cluster, but also between distinct clusters. To realize cluster synchronization, an incorporate method integrating event-triggered communication and pinning control is proposed. By using Lyapunov stability theory and inequality analysis, some sufficient conditions on cluster synchronization method will be derived in this paper. In addition, an original optimizing algorithm with wider applicability for nodes selection is proposed to solve the obstacle for pinning criterion. Two numerical illustrations will be given to validate the theoretical analysis results.