Synchronization of Nonlinear Coupled Networks via Aperiodically Intermittent Pinning Control

In this paper, pinning synchronization problem for nonlinear coupled networks is investigated, which can be recurrently connected neural networks, cellular neural networks, Hodgkin-Huxley models, Lorenz chaotic oscillators, and so on. Nodes in the network are assumed to be identical and nodes' dynamical behaviors are described by continuous-time equations. The network topology is undirected and static. At first, the scope of accepted nonlinear coupling functions is defined, and the effect of nonlinear coupling functions on synchronization is carefully discussed. Then, the pinning control technique is used for synchronization, especially the control type is aperiodically intermittent. Some sufficient conditions to guarantee global synchronization are presented. Furthermore, the adaptive approach is also applied on the pinning control, and a centralized adaptive algorithm is designed and its validity is also proved. Finally, several numerical simulations are given to verify the obtained theoretical results.