Hybrid synchronization of the general delayed and non-delayed complex dynamical networks via pinning control

This paper investigates the hybrid synchronization problem of two coupled complex dynamical networks with non-delayed and delayed coupling by the pinning control strategy. Based on the LaSalle invariance principle and linear matrix inequality technique, we obtain some sufficient conditions for the hybrid synchronization by applying the simple linear feedback and adaptive controllers to a part of nodes. Under suitable conditions, two coupled networks can reach the hybrid synchronization, i.e., the outer synchronization between the drive and response networks, and the inner synchronization in each network simultaneously. Numerical simulations show the effectiveness of the proposed synchronization scheme.