Inter-layer generalized synchronization of two-layer impulsively-coupled networks

Abstract

In the last decade, synchronization of complex dynamical networks via impulsive control has been studied by many researchers. Much attention has been paid to inner synchronization in a single network or complete outer synchronization between two single networks. So far, there have been few research results on generalized synchronization (GS) between two impulsively coupled complex networks with different node dynamics and network topologies. In this paper, inter-layer GS of two-layer impulsively-coupled dynamical networks with uncertain parameters by means of impulsive control is studied. The synchronization strategy and parameter updating laws for inter-layer generalized synchronization based on the auxiliary system method are proposed. Furthermore, it is found that the stable region with respect to network parameters guaranteeing generalized synchronization relies on the intra-layer coupling strength of the response-layer network and the impulse gain matrix. In particular, the stable region narrows with the increase of the coupling strength of the response-layer network, and enlarges as the impulse gain is closer to −1.