Synchronization for coupled reaction-diffusion neural networks with and without multiple time-varying delays via pinning-control

The synchronization problem for two types of coupled reaction-diffusion neural networks (CRDNNs) with and without time-varying delays is considered in the article. By utilizing pinning control technique and choosing appropriate Lyapunov functionals, we analyze synchronization of these network models. Firstly, by using some inequality techniques, a synchronization criterion is derived for CRDNNs. Secondly, in order to obtain appropriate coupling strength, an adaptive strategy is also developed. Furthermore, we generalize these results to the model of CRDNNs with multiple time-varying delays. Two illustrate examples including numerical simulations are presented to indicate the correctness of our results.