Research On Multilayer Network Structures And Synchronizability

Complex network is the abstraction and description of complex system,is the basis and tool to study and understand the nature and function of complex system,and is also an important content of network science research.Since the upsurge of complex network research in the 1990 s,rich research results have been achieved after nearly 30 years of development.However,until now,most of the research results of complex network are concentrated on the single network(or single-layer network).With the development of modern complexity science,single-layer network can not meet the needs of the actual complex system research.The actual complex system often has a large number of nodes,the corresponding network structure is very complex,showing a variety of network interdependence,interaction complex relationship,people call this kind of network ”network” or multilayer network.Multilayer network can more accurately reflect the interaction between multiple networks and the physical process inside the system in the actual complex system,which has become one of the important front directions of network science research.Synchronization is a very common and important non-linear phenomenon in complex systems,which widely exists in biology,physics,chemistry,medicine,communication,economy,electricity,social systems and other fields.The synchronizability of complex networks,especially large-scale networks,needs to be further explored.Based on the above background,this paper uses the complex network theory,graph theory,matrix theory and other theories and methods,as well as numerical simulation experiment methods,to carry out in-depth research on the structure and synchronization of multilayer complex network.The main research contents are summarized as follows:(1)Research on synchronizability based on multilayer chain network.Theoretically,the eigenvalue spectrum of two kinds of multilayer chain networks is derived strictly,and the relationship between the synchronizability and the structural parameters(i.e.,number of nodes,intralayer and interlayer coupling strengths,number of layers)of the networks is analyzed.The simulation results are consistent with the theoretical analysis.(2)Research on synchronizability based on multilayer star and star-ring networks.In theory,the analytic expressions of the eigenvalues spectrum of multilayer star and star-ring networks are derived strictly.We analyzed the relationship between the synchronizability and structural parameters(i.e.,number of nodes,intralayer and interlayer coupling strengths,number of layers)of these two networks under different coupling strength between layers by using the master stability function(MSF)theory.Finally,numerical simulations demonstrated the validity of the theoretical results.(3)Research on the synchronizability based on two-layer cluster ring networks.Extending the cluster ring network to the two-layer network model.The inner structure of the clustering ring is small world,random and scale-free.Through a large number of simulation experiments,we study the influence of the scale change,the coupling strength between layers and the probability change of the connection between layers on the synchronizability.