Topology Identification For Multi-layer Complex Dynamical Networks

In nature,society and engineering practice,the topology of the network is often unknown,partially unknown or uncertain.However,the topology of the network plays a key role in determining the evolution mechanism of the network and predicting the dynamical behavior of the network.Therefore,the research on network topology identification has important practical significance and broad application prospects.In recent years,with the continuous deepening of research on complex dynamical networks,people have gradually realized that most networks in real society and engineering do not exist independently,but are related to other networks in structure or function,and become the multilayer network.Since a single-layer complex dynamical network can not simulate the true characteristics of the network well,and the multi-layer complex dynamical network can better understand the evolution of the network,the research on the single-layer complex dynamical network can no longer meet the actual needs.Based on the above discussion,this paper takes the multi-layer complex dynamical network as the research object,and proposes several new topology identification schemes for multi-layer complex dynamical network.Through the idea of constructing the drive and response networks,the adaptive feedback identifier is designed,so that the response network and the drive network are synchronized,and the topological structure of the original drive network is identified.The main findings of this paper are as follows:Firstly,for the multi-layer complex dynamical network model with the same number of nodes in each layer and one-to-one correspondence between nodes,the topology structure identification problem is studied.First of all,the original network is regarded as a drive-end network.In order to identify the topological structure of the drive network,a response-end network with an adaptive feedback identifier is constructed to obtain an error dynamic network.Then,Lyapunov stability theory and La Salle's invariance principle are used to prove the gradual stability of the error dynamic network,so that the response end network and the drive end network are synchronized,and the topological structure of the drive end network can be identified by the response end network.Finally,the effectiveness of the proposed topology identification scheme is verified by Matlab numerical simulation.Secondly,aiming at the multi-layer complex dynamical network model with the same number of nodes in each layer and arbitrary connection between the nodes,the topology identification problem is studied.Based on the research method of nodes one-to-one correspondence model,using the idea of constructing drive and response networks,the multi-layer complex dynamical network with arbitrary connection of nodes is identified.Since the coupling delay is common,the intra-layer coupling delay is introduced into the model,and the validity of the above model is verified by the numerical simulation of the two-layer network through Matlab.Thirdly,aiming at the multi-layer complex dynamical network model with different types and numbers of nodes in each layer and arbitrary connection of nodes between layers,the topology identification problem is studied.Based on the research of the model with the same number of nodes in each layer,it is extended to a multi-layer complex dynamic network model with different types and numbers of nodes in each layer.Based on the research of multi-layer complex dynamical network with intra-layer coupling delay,it is extended to the complex dynamical network model with intralayer and inter-layer coupling delay.The effectiveness of topology identification of the above models is verified by Matlab.