Pinning synchronization of spatial diffusion coupled reaction-diffusion neural networks with and without multiple time-varying delays

In this paper, two coupled reaction-diffusion neural networks (CRDNNs) with spatial diffusion coupling are studied. In the first one, the single reaction-diffusion neural network (RDNN) is coupled by their current states. The single RDNN is coupled by their current states and delayed states in the second one. Combined with some inequality techniques and Lyapunov functional approach, a synchronization criterion for the first network model is established via adding controllers to the first l nodes. In addition, a sufficient condition is derived to make sure that the considered network can achieve synchronization by designing pinning adaptive feedback controllers. Similarly, the pinning synchronization for the second network model is also considered. Finally, the correctness of the obtained results are confirmed by numerical simulation in two illustrated examples.