On pinning synchronization of complex dynamical network with coupling delay

We present some pinning criteria for synchronization of complex network with coupling delay. We answer the challenging problems in pinning synchronization of complex networks: (1) What types of pinning schemes may be chosen for a given complex to realize synchronization? (2) What kinds of controllers may be chosen to ensure the network synchronization? (3) How large should the coupling strength be used in a given complex network to achieve synchronization? There is large different from the complex network without delay because of the existing of delay. The complex network without delay must be synchronization if and only if the coupling strength is large enough. But for the complex network with delay existing in the node coupling, there exists optimum interval in the overall coupling strength ensuring the stability, which provides the important theoretical foundation for the study of anti-synchronization.