Asymptotically Local Synchronization of an Interdependent Network with Two Sub-Networks and Delays

In this article, the asymptotically local synchronization for a general interdependent dynamical network with two sub-networks and delays is investigated. The coupling function under consideration in this network is continuous and on behalf of both the intra-network and inter-network. Based on the Master Stability Function method, Linearization method and Lyapunov-Krasovskii Stability Theory combing with the Delay Differential Inequality technique, some elegant strategies are established which guarantee the asymptotically exponential local synchronization for each node in the network. Finally, several numerical simulations show the effectiveness and feasibility of the proposed schemes.