Lag synchronization of complex dynamical networks with hybrid coupling via adaptive pinning control

In this paper, the problem of the lag synchronization between two general complex dynamical networks with mixed coupling by pinning control is studied. Based on the Lyaponov functional theory and mathematical analysis method, less conservative conditions of lag synchronization are obtained by adding the controllers to part of nodes. Moreover, the coupling configuration matrices are not required to be symmetric or irreducible. It is shown that the lag synchronization of the drive and response systems can be realized via the linear feedback pinning control and adaptive feedback pinning control. These results remove some restrictions on the node dynamics and the number of the pinned nodes. Numerical examples are presented to illustrate the effectiveness of the theoretical results.