Research On Synchronization Capability Of Multilayer Network Based On Vital Nodes

Complex network is a network with some or all of the characteristics of selforganization,self-similarity,attractors,small worlds,and scale-free.The study of complex networks can help people understand the types of networks that exist in our lives.Complex network has high research value,because it has a strong ability to interdisciplinary integration and a wide range of applications.Synchronization is a natural phenomenon in nature and human society.It plays a very important role in many aspects such as physics,clinical medicine,and chemistry.In recent years,more and more scholars are pay attention to complex network synchronization,and they have done a lot of research based on the synchronization of single-layer networks.But in real life networks,there are not only single-layer,but also many double-layer and even multi-layer networks,such as some special social networks.In order to study the networks that are more suitable for life,scholars began to study the synchronization of multi-layer networks.In this dissertation,the main work can be listed as follows:First,this dissertation uses the master stability method to theoretically derive the synchronizability of a three-layer and multi-layer fully-coupled network and their simplest equivalent network.The result proves that both the three-layer and the multilayer fully-coupled network have the same synchronizability as their corresponding simplest equivalent network.In order to verify the correctness of the derivation results,a three-layer and five-layer fully coupled network and their corresponding simplest equivalent network model are established.And by simulating the synchronization process on the model,the correctness of the derived results was confirmed.Then,this dissertation analyzes the five influencing factors that affect the multilayer fully coupled network.These five factors are: intra-layer coupling strength,inter-layer coupling strength,the number of nodes in each layer of the network,the number of key nodes,and the number of layers in the network.When the synchronized region is unbounded,the synchronizability increases with the increase of the inter-layer coupling strength,the number of nodes per layer network,the number of vital nodes and the number of network layers,but the intra-layer coupling strength has little effect on the synchronizability of the network.When the synchronized region is bounded,the synchronizability increases with the decrease of the inter-layer coupling strength,the inter-layer coupling strength,the number of nodes per layer,the number of vital nodes,and the number of layers in the network.Finally,this dissertation explores the effect of increasing the number of network layers on the synchronizability of complex networks.Experimental results prove that when the synchronized region is unbounded,the smaller the size of the network,the more obviously the synchronizability of the network increases with the number of network layers.And when the synchronized region is bounded,the larger the network size,the more obviously the synchronizability of the network increases with the number of network layers.At the same time,when there are fewer connections between layers,appropriately increasing the number of network layers can increase the synchronizability of the network.However,when the number of connections between layers exceeds a certain range,increasing the number of network layers will not enhance the synchronization capability of the network.