Inner-Outer Synchronization Analysis of Two Complex Networks with Delayed and Non-Delayed Coupling

Abstract

In this paper, two kinds of synchronization between two complex networks with non-delayed and delayed coupling are discussed by the pinning control method, that is, inner synchronization and outer synchronization. Based on the Lyapunov stability theory and linear matrix inequality (LMI), some sufficient conditions for the synchronization are derived by adding linear feedback controllers to a part of nodes, and the linear feedback controllers are designed. Under suitable conditions, not only inner synchronization but also outer synchronization can be asymptotically achieved. Numerical simulations are presented to show the effectiveness of the proposed synchronization scheme.