Edge Weight Allocation And Synchronization Optimization Of Multi-layer Networks Based On Spectral Graph Theory

In the real world,many physical cybernetical networks,such as transportation networks,circuit networks,social networks need to be described as multi-layer networks.Synchronization of networks has always been one of the most important dynamic behaviors and has important embodiment and practical value in various fields.To a large extent,the characteristics of multi-layer network are reflected in the role of inter-layer connection.The number and type of inter-layer connection edges have a great impact on the synchronization of the whole network.How to design inter-layer connection and allocate edge weights for inter-layer connection are the key to design a multi-layer network.This paper aims to give the synchronization optimization strategy of multi-layer network and deduce the synchronization theory in multi-layer network layer using spectral graph theory.For a given two-layer network topology,this thesis redistributes edge weights from the perspective of graph theory to improve the synchronizability of multi-layer networks.At present,most researches on multi-layer networks assume that the intra-layer edge weights or inter-layer edge weights are the same,but the work in this paper is different from this.Using graph comparison method,we assign different weights to different edges according to the topological characteristics of two-layer networks,which is consistent with the actual situation of most networks.Furthermore,numerical experiments are carried out on typical two-layer networks and real-world networks,and their synchronizability are compared under different edge weight allocation strategies.The results show that edge weight distribution using the graph comparison method can achieve better performance compared with uniform distribution,degree correlation distribution and edge betweenness distribution.In addition,this thesis proposes a multi-layer network model with different dynamics,which allows different layers to have different dynamics functions.Lyapunov stability theory is used to study the intra-layer synchronization of multi-layer networks with different types of inter-layer connections.From the perspective of spectral graph theory,we have constructed the requirement of edge weights to realize synchronization of multi-layer networks.Focusing on the influence of inter-layer connection on network synchronization,we find that even if a single network cannot be synchronized,when inter-layer coupling strength is large enough,the two-layer network can achieve intra-layer synchronization.Under the two-layer network model,we can realize the synchronization of the whole network by distributing weights for one layer and improving inter-layer edge weight,which provides ideas for synchronization control of multi-layer networks.