Generalized Synchronization Control In The Multilayer Networks By Pining Strategy

Complex networks exist widely in real life.The theory and application of complex networks have been developed rapidly in recent years.A complex network is composed of many independent nodes with a certain structure,and the connections between nodes have a complex structure.At present,the dynamic behavior of complex networks,such as stability,synchronization and control,have become one of the most concerned problems.The control of complex network refers to the use of the network’s own structure,artificial influence on the network,so that the network to achieve the desired state.Therefore,putting forward a simple and practical complex network control method to realize network control is the key of research.In addition,in many practical problems,networks interact with each other,so the interaction between multi-layer complex networks has also aroused people’s extensive attention.The synchronization phenomenon of network exists widely in nature and has always been a concern of scholars.With the development of the theory of multilayer complex networks,the generalized synchronization of multilayer networks has been paid more attention.At present,most synchronization control methods of complex networks use the error between the driving signal and the response signal as the control signal to realize the generalized synchronization of the network.In order to realize the generalized synchronization of the network,sometimes the controlled node may not be the key node reflecting the correct relationship between the two networks,so the obtained synchronization results cannot correctly reflect the relationship between the two networks.In this paper,the generalized synchronization of multilayer complex networks is studied,and a new method of multilayer complex network checking control and adaptive checking control is proposed.By using the auxiliary system method,the generalized synchronization is realized by adding the interaction between the response network and the auxiliary network.In this method,there is no direct relationship between the control signal and the drive signal,which will reduce the influence of some non-important drive signals on the response network.In order to reduce the number of controllers,reduce the complexity and ensure the convergence and stability of the network,how to select the pining nodes and the number of pining nodes are discussed extensively.Numerical experiments verify the effectiveness of the proposed method.