Research On The Modelling Of Two-layer Dynamic Neural Networks And Synchronization

The synchronization of complex networks has a great theoretical research value in the area of biology,medicine,physics,communications,power systems and other fields,which is closely linked to our daily lives.The further study on complex networks not only helps us to understand a variety of social behavior,physiological activities and even technology phenomena,but also promotes the development of many new branches of science and interdisciplinaries,which leads to fundamental changes to the way the human live.Therefore,the crossover study between the synchronization of complex networks and other subjects has attracted a wide attention in scholars.Along with the development of complex networks,the priority has changed from the single-layer networks to multilayer networks which are more close to the actual networks.Increasingly studies have shown that neural networks,especially the brain network have small-world properties.So in the process of modeling a neural network,a single neuron unit can be regarded as the node of the network,then the neuron units are connected to others in a specific way that contains small-world network properties.Star coupled networks,as a kind of special regular network with small-world properties,conform to the structural characteristics of brain networks.So the research mainly focuses on the synchronization of the two-layer network..The recent multilayer network synchronization researches are mainly concentrating on undirected and unweighted regular networks,such as two layers of undirected and unweighted star networks.Based on the undirected and unweighted star networks,the study develops a two-layer directed and unweighted star network model,then builds the Super-Laplacian matrix of that model.Using the method of master stability function,eigenvalues of the Super-Laplacian matrix are calculated and the dynamic parameters of the two-layer directed and unweighted star network are analyzed in different regions of synchronization.The unweighted network can only reflect the connecting relation and topology characteristics of different nodes,it cannot describe the strength of the interaction between the nodes.In order to create a more realistic network model,the study,on the basis of two-layer unweighted star networks,creates the undirected and weighted star network model as well as the directed and unweighted star network model.Then,the relation between synchronization and the parameters is comprehensive discussed,and methods that can change the synchronization have been proposed in the study.Finally,the synchronization of two-layer complex networks based on the BA model is preliminarily analyzed.