Synchronization of delayed neural networks with hybrid coupling via partial mixed pinning impulsive control

This paper investigates the synchronization problem of a class of general hybrid coupling delayed neural networks with internal delay as well as coupling delay. A general hybrid coupling term involving current-state coupling, discrete-delay coupling and distributed-delay coupling is considered. The partial mixed pinning impulsive control is proposed for achieving synchronization, which is combined with the advantage of pinning impulsive control and two impulsive effects simultaneously (i.e. synchronization and desynchronization). In order to handle the difficulties of multi-time delays, some generalized differential inequalities about time-varying delays are established. By using Lyapunov functional method and applying a mixed pinning impulsive control scheme, some sufficient conditions are derived to guarantee global synchronization of the neural networks. Moreover, our results can cover and extend the previous related works. Finally, numerical examples are also given to illustrate the efficiency of our methods and the theoretical results.