Synchronization analysis of hybrid-coupled delayed dynamical networks with impulsive effects: A unified synchronization criterion

This paper addresses the problem of globally exponential synchronization for a class of general hybrid-coupled impulsive delayed dynamical networks with both internal delay and coupling delay. A more general delayed coupling term involving the transmission delay and self-feedback delay is considered. Additionally, two types of impulses occurred in the states of nodes are taken into account: (i) synchronizing impulses defined as they can enhance the synchronization of dynamical networks; and (ii) desynchronizing impulses meaning that they can suppress the synchronization of dynamical networks. By establishing an improved impulsive differential inequality derived based on the average impulsive interval approach, a simpler and less conservative unified globally exponential synchronization criterion is obtained, which is simultaneously effective for synchronizing and desynchronizing impulses. It is shown that the obtained criterion is closely related with impulse strengths, average impulsive interval, and topology structure of the networks. Finally, numerical examples including a typical nearest-neighbor unidirectional coupled network and a scale-free network are given to demonstrate the applicability and efficiency of the theoretical results.