Adaptive pinning synchronization of coupled neural networks with mixed delays and vector-form stochastic perturbations

In this article, we consider the global chaotic synchronization of general coupled neural networks, in which subsystems have both discrete and distributed delays. Stochastic perturbations between subsystems are also considered. On the basis of two simple adaptive pinning feedback control schemes, Lyapunov functional method, and stochastic analysis approach, several sufficient conditions are developed to guarantee global synchronization of the coupled neural networks with two kinds of delay couplings, even if only partial states of the nodes are coupled. The outer-coupling matrices may be symmetric or asymmetric. Unlike existing results that an isolate node is introduced as the pinning target, we pin to help the network realizing synchronization without introducing any isolate node when the network is not synchronized. As a by product, sufficient conditions under which the network realizes synchronization without control are derived. Numerical simulations confirm the effectiveness of the obtained results.