Complete Synchronization And Stability Of A Two-layer Star Complex Network

Synchronization is a phenomenon that is common in nature and society.Synchronization of complex networks has a wide range of applications in physics,chemistry,bio-vibrators and economics.In recent years,with the in-depth study of complex networks,people have realized that most networks in reality do not exist independently,but they are structurally or functionally interdependent with other networks.Thus a multi-layer network is formed.The network has become one of the most cutting-edge research directions in today's complex network fields,and the star network is the most widely studied.Based on the double-layer star-shaped complex networks model proposed in[1,3],this paper redefines two types of double-layer star-shaped complex network models according to the different connection forms of nodes in the two networks.The synchronization of the star-shaped networks is investigated using linear stability analysis.The stability of the star-shaped complex networks with Logistic mapping coupling is discussed.The stability conditions of the networks synchronization arestrictly derived.The cross-sectional stable region of the synchronous manifold on the parameter plane is studied.The influence of the edge change on the stable region is also discussed.The results show that the connection edge between the central nodes of the inter-layer and the non-central node will increase the stable region of the networks.Further,this paper studies the effect of inter-layer coupling strength on the synchronous stable region when the inter-layer coupling strength is different.