Research On The Influence Of Topological Structures Of Complex Networks On Propagation Dynamics

The dynamics characteristics of network-based propagation models have received extensive attention from experts and scholars.As the basic elements of a complex network,nodes and links are the low-order structural units that constitute the network framework.As a result,we first study the importance of the nodes and links of a network.We obtain the node importance indicators,and the indicators can be applied to both the undirected network and the directed network,which can describe not only the transmissibility of a node but also its infectivity.We then obtain the characteristic of the optimal link structure that promotes network propagation.It is of great significance to the research on the inverse problem of reconstructing complex networks based on specific dynamic characteristics and provides an important reference value for the analysis and control of network propagation.However,for actual social contagion,the pairwise interaction between nodes is easy to form a group and a layer structure.Therefore,we study the propagation model of a bilayer coupling network with a group structure,thereby further expanding the application direction of bilayer network propagation dynamics.In addition to the pairwise interactions between nodes,high-order interactions are also widely present in complex social systems.Accordingly,we introduce simplicial complexes to study the influence of the high-order structure on the propagation dynamics,and then we further explore the coupling process of opinion fusion and information transmission,which provides a new research perspective for describing the high-order structure of the network and describing complex dynamic behaviors.The main research contents are as follows:Firstly,for the basic structure of a complex network,we study the node centrality indicators and the adding strategy of optimal links.According to the network propagation model,we derive the node transmissibility and infectivity indicators based on the dynamic equation and further obtain the natural energy indicator.Through numerical simulations,it is found that when the node’s infectivity is strong,the infection rate coefficient needed to reach a given state is smaller;When the node’s transmissibility is strong,it makes the network reach a given state in less time.By conducting Taylor expansion to the proposed natural energy,we found that the propagation performance of a class of undirected networks is better than that of its corresponding directed networks.In addition,based on the matrix perturbation method,by adding a link to the original network,the difference of spreading prevalence before and after adding a link is induced,then the maximum value of spreading prevalence increase and the corresponding network topology are obtained,and thus the optimal link adding strategy to promote propagation is proposed.The effectiveness of the proposed strategy is verified by numerical experiments.By introducing network configuration model,rich club coefficient and Pearson coefficient,it is found that degree correlation can lead to the cross phenomenon of network propagation.Then,for the widespread group structure,we study the influence of group structure characteristics on disease transmission in bilayer network coupling propagation dynamics.A bilayer network with group structure is constructed,and then a coupling propagation model is established based on Markov chain method.The bilayer network is divided into information layer and physical layer,which corresponds to the process of information diffusion and disease transmission.By constructing probability transfer trees,the following propagation process is described: information diffusion in information layer can inhibit disease transmission in physical layer through feedback mechanism between layers,disease transmission in physical layer can promote information diffusion in information layer,and intra group and inter group transmission have different infection rate coefficients.Through numerical simulations,it is found that the increase of group size of information layer is conducive to the spread of disease,and the increase of group size of physical layer is conducive to the spread of disease.Furthermore,the transmission threshold of disease outbreak is derived.Compared with the standard multiplex networks,it is found that the network with group structure has better propagation performance and robustness by introducing percolation theory.Furthermore,for the high-order structural characteristics of complex networks,we study the SIRS model based on the high-order structures and nonlinear incidences.By reconstructing the complex network-based system into a high-order simplicial complex and coupling the high-order structure with the nonlinear incidence,we build a high-order spreading model.Through a large number of simulations on the simplicial complex of the real-world network and the synthetic network,we find that the propagation dynamics based on the simplicial complex occurs many phenomena that cannot be described by the standard network propagation model,including bistable state,discontinuous transitions,and periodic outbreaks of diseases.In order to further analyze the above phenomenon theoretically,under the assumption of homogeneity,we adopt the mean-field method to simplify the model,and then obtain the dual threshold of disease outbreak and the necessary conditions for the existence of bistable state through theoretical analysis.By stability analysis theory,we investigate and obtain the stability of each equilibrium state of the simplicial model.We obtain that the discontinuous transition and the phenomenon of disease periodic outbreaks are determined by the high-order structural characteristics of the system and the nonlinear incidence of the dynamics.Finally,for the high-order and low-order coupling characteristics of a network,we study the coupling propagation dynamics of view fusion and information transmission.The simplicial complex is used to describe the group structure of complex networks,and a coupling process with view fusion and information transmission is constructed,in which views are communicated and fused within groups,and information is exchanged between groups.When the number of individuals that have known the information in the simplex is no less than a certain given threshold,the state of the simplex is set to the known state,otherwise it is the unknown state.The Markov chain method is used to model the above-mentioned coupling propagation process,in which intra-simplex communication and inter-simplex information exchange are characterized by different propagation parameters.By mathematical calculation,we derive the propagation threshold of the proposed model.At the same time,we perform extensive numerical experiments to verify the model and method,and thus find and explain the jump phenomenon in the dynamic process of the coupling simplicial model.