Model Construction Of Multilayer Directed Network And Analysis Of Its Propagation Dynamics

With the development of complex network research,more and more complex systems can be abstracted into the form of multilayer directed network,which includes multiple subsystems and connection layers.The multilayer directed network model focuses on describing the diversity,difference and direction between the nodes of the network,it can also be used as a model tool to analyze some characteristics of the network.Therefore,the problem brought by multilayer directed network is to generalize the model,and study multilayer and directed system by establishing a solid foundation and new related tools.In recent years,a lot of work has been done to understand the structural and dynamic properties of such systems,especially the interaction between propagation dynamics and topology.In the study of transmission dynamics,it is of great significance to study the transmission process of infectious diseases among the three groups.In view of the above problems,the thesis is from the perspective of the generation of infectious disease transmission characteristic model,transmission conditions and transmission influence in multilayer directed network,three kinds of three-layer directed network models and three kinds of cyclic three-layer directed network models are constructed,combined with theory and simulation,the degree distribution characteristics of six network models,the influence of transmission characteristics such as transmission cycle and outbreak threshold of infectious diseases are analyzed.The specific research contents are as follows:1.The three-layer directed network and cyclic three-layer directed network models are constructed and their characteristics are analyzed.Combined with the traditional complex network theory,three three-layer directed network models and three cyclic three-layer directed network models are constructed,by controlling the number of directed links between levels,the network structure with multimodal characteristics is configured.Combined with numerical simulation,the change of the number of links between the layers of directed network makes the network degree distribution characterize the characteristics of single peak,double peak and three peak;combining the optimization mechanism and the change of the number of inter layer links,the network characteristics show the coexistence of power law and single peak.2.This thesis constructs the framework of three-layer directed network and circular three-layer directed network propagation model.This thesis attempts to embed the classical propagation mechanism into the network model constructed,and analyze the influence of different propagation conditions on the network,under the condition that the nodes in the layer and the internodes are tightly or sparsely interconnected.This study found that: close interlayer connection promotes the spread of infectious diseases;when the recovery rate remains unchanged,the infection density and propagation speed are directly proportional to the propagation rate.When the propagation rate remains unchanged,the infection density and propagation speed are inversely proportional to the recovery rate.3.The immune strategies of three-layer directed network and circular three-layer directed network propagation model are studied.By considering the importance of out degree and in degree in directed networks,use the average in-degree value,the average out-degree value and the node in-degree value corresponding to the peak value shown in the in-degree distribution diagram,and puts forward neighbor immunity and hybrid immunity,which are verified by numerical simulation.