Synchronization of coupled reaction-diffusion neural networks with hybrid coupling via aperiodically intermittent pinning control

This paper investigates the complete synchronization for linearly coupled neural networks with time-varying delays and reaction-diffusion terms by using the aperiodically intermittent pinning control. The coupling matrix for the network can be asymmetric. Compared with state coupling in the synchronization literature, we design a novel distributed coupling protocol by using the reaction-diffusion coupling: spatial coupling, which can accelerate the synchronization process. This can be regarded as the main difference between this paper and previous works. Using the Lyapunov function and theories in the aperiodically intermittent control, we present some criteria for the complete synchronization with a static coupling strength. In this case, there is no constraint on the bound of time-varying delays, so it can be larger than the length of control span. On the other hand, we also consider the network with an adaptive coupling strength. In this case, the infimum of the control time span should be larger than the upper bound of time delay. Numerical simulations are given to show correctness of obtained results.