Synchronization for Complex Networks With Multiple State or Delayed State Couplings Under Recoverable Attacks

In this article, we, respectively, take the synchronization into consideration for directed and undirected complex networks (CNs) with multiple state or delayed state couplings subject to recoverable attacks. By selecting appropriate Lyapunov functional, employing inequality techniques, and adopting the designed state-feedback controller, two criteria of the synchronization are established for the directed CN with multiple state couplings (CNMSCs). Moreover, the synchronization of CNMSCs is also discussed for the case that the network topology is undirected. In addition, two types of CNs with multiple delayed state couplings are also proposed, and several criteria of synchronization are formulated for these networks. Finally, two examples are given to verify the correctness of the derived synchronization criteria.

Automated summary

This article investigates the synchronization problem for directed and undirected complex networks with multiple state or delayed state couplings, subject to recoverable attacks. Synchronization criteria are established using Lyapunov functional, inequality techniques, and state-feedback controller. The article also discusses the synchronization of networks with multiple delayed state couplings.