Modeling Study On Propagation Behavior In Complex Social Networks Based On Dynamical System

The spread of infectious diseases and the spread of rumors are two common and important spreading behaviors in complex social networks,and they are closely related to human life.It has important theoretical and practical significance for the stability and development of human society to study on the dynamics behavior and transmission rules of infectious diseases and rumors and then to formulate effective prevention and control strategies.Spreading dynamics is a theoretical method to study the spread of infectious diseases and rumors quantitatively.Firstly,the propagation process is modeled according to the communication mechanism.Then the dynamics behavior of the model is studied qualitatively and quantitatively,the development trend is predicted,and the main causes and factors of the spread are analyzed.Finally,the effective prevention and control strategy is designed according to the analysis results.The propagation process in social network is affected by propagation mechanism,network topology,communication content and personal behavior characteristics,etc.Based on the theories of complex system,the ideas and methods of infectious disease dynamics and sociology,this paper studies the spread of infectious diseases and rumors in social networks.Considering network topology and the propagation mechanism of propagation behavior,suitable propagation models are established,and the dynamics behavior of the propagation model is analyzed by using the qualitative and stability theory of differential equations and stochastic simulation.Finally,the corresponding control measures are put forward.The main research contents and findings are as follows:Considering the impact of the average infection period on the spreading behavior of infectious diseases,we establish SIS dynamics models with recovery time delay on homogeneous and heterogeneous complex networks respectively,the equilibrium point of the model is calculated,and the threshold of the epidemic is obtained.Then the stability of the equilibrium point is analyzed by the stability theory.Finally,the conclusion is verified by simulation,and the influence of the average infection period and the network structure on the spread of infectious disease is revealed.In order to investigate the impact of extrinsic incubation period on the spreading behavior of vector-borne diseases,according to the transmission mechanism of vector-borne disease and the network topology,a coupled dynamical system is established by means of mean field theory.A SIS model with time delay is obtained through dimensionality reduction.The propagation threshold of the model is analyzed.It is proved that the two equilibrium points of the model are globally asymptotically stable.The influence of network structure and extrinsic incubation period on propagation dynamics is analyzed by numerical simulation.In order to investigate the impact of nonuniformity of community sizes on rumor propagation behavior.Firstly,a network generation model is given to generate scale-free networks with non-uniform community structure.On the generated networks,dynamics behavior of rumor spreading is simulated by Monte Carlo in the case of single source.The influence of the bridge hubs,nonuniformity of communities and the strength of community structure on the dynamics behavior of rumor propagation is revealed.In order to investigate the influence of the rumor spreaders on complex social networks,based on the classical rumor propagation model,we assume that each individual contacts all his neighbors at each time step and propagation rate is different.Firstly,according to the different characteristics of the networks different node ranking methods are adopted to rank and layer the network nodes.Then,Monte Carlo method is used to simulate rumor propagation,and the propagation performance of nodes in different layers as source nodes and informed nodes is analyzed.Finally,influential rumor spreaders in social networks are identified to show that there exist influential rumor spreaders in social networks.