Event-triggered pinning passivity and synchronization of multiple spatial diffusion coupled reaction–diffusion neural networks

In this paper, the problem of the event-triggered pinning passivity and synchronization for multiple spatial diffusion coupled reaction–diffusion neural networks is investigated. Two types of multiple spatial diffusion coupled reaction–diffusion neural networks, with undirected and directed topologies, are considered. Combining the advantages of event-triggered and pinning control methods, event-triggered pinning controllers for these two networks are constructed. By imposing appropriate Lyapunov functionals and inequality techniques, several passivity and synchronization conditions are established for these two networks under the designed event-triggered pinning controllers. Moreover, the non-occurrence of the Zeno behavior in the proposed control is proved. Two numerical examples are illustrated to verify the effectiveness of the proposed criteria.