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

•Over the past decades, complex dynamical networks have attracted tremendous research interests from various disciplines. However, the existing single network model is insufficient to describe the characteristics and dynamics of these complex systems. Therefore, the multi-layer complex network model which tallies with the actual features has been put forward. In this paper, the two-layer impulsively-coupled network model, such as two-layer social communication network, is given and studied.•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, the synchronization strategy and parameter updating laws for inter-layer generalized synchronization, which is defined as harmonious coexistence between a node in one layer and its corresponding nodes in other layers, are proposed by means of the auxiliary system method.•We find that the feasible stable region guaranteeing inter-layer synchronization relies on the intra-layer coupling strength of the response-layer network, the impulse gain matrix and the impulsive interval•The feasible 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. 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 re