Static pinning synchronization in dynamical networks with event-triggered coupling: Average delayed impulsive weight approach

Abstract

This paper studies the synchronization of coupled neural networks (NNs) using static pinning impulsive control, which incorporates stability delays and event-triggered coupling mechanism. The term “static pinning” refers to a fixed set of pinned nodes throughout the control process. The pinned layer and follower layer are employed to depict the hierarchical structure generated by each static pinning strategy. Based on hierarchical structure, the time delay information present in the impulses is effectively extracted through the static pinning control and integrated into the synchronization of the pinning layer, and follower layer, utilizing an event-triggered coupling mechanism. The study establishes flexible criteria that ensure synchronization for coupled NNs while excluding the Zeno behavior. In addition, the pinning layer is equipped with time-delay free impulsive control input with asynchronous actuation, and the synchronization of coupled NNs are also obtained. The results show that the delays in the pinning impulsive control input contribute significantly to the synchronization of pinning layer. Finally, the simulation results are given to illustrate the effectiveness of the control method.