Synchronization of delayed complex-valued networks via aperiodically intermittent pinning control

In this paper, the synchronization problem for linearly coupled complex networks is investigated, which is denoted by ordinary differential equations with complex-values. The coupling topology can be asymmetric, and the time delay also exists in the network model. By pinning some external aperiodically intermittent control on the network nodes, we will prove that under some conditions, the complete synchronization will be finally realized exponentially. Moreover, applying the adaptive technique on the coupling strength, we will also present an adaptive rule, whose validity is rigorously proved. Finally, some numerical simulations will be given to illustrate the correctness of these obtained results.