Dynamic Analysis Of Information Spreading Model Based On Scale-free Networks

Spreading dynamics based on complex networks theory can be used to describe many important activities in the real world,including the outbreak of epidemics,the spread of news,ideas and technological innovation,the promotion of commodities and the rise of political movements.Understanding the underlying mechanisms of various types of transmission in complex networks is essential for the application of epidemiology,marketing,group dynamics and network stability in different fields.This paper proposes several kinds of new information spreading dynamics models based on scale-free networks.The background of each model is combined with practicalities,and various mechanisms and specific situations in the process of information spreading are considered as much as possible.We deduce and analyze the threshold and stability of the model in detail,and validate the theoretical results through simulation and make some extended explorations.The contributions and innovations of this paper are mainly divided into three parts:（1）Based on the process of rumor spreading in social networks,we propose and study a SEIR rumor spreading model with feedback and hesitation mechanism.Based on classical warehouse model and mean field theory,we obtain the basic reproduction number R₀ and the equilibriums of the system,and study the relationship between the basic reproduction number and the degree distribution of the network and the migration of people.The global stability and the global attractiveness of the equilibriums where rumor information prevails in are proved in detail.In addition,we also study the attraction and ambiguity of rumors,and propose an improved model of social network feedback mechanism.We also discuss the impact of feedback mechanism on the dynamic process of rumor spreading.The numerical simulation confirms the above analysis results.（2）Considering the actual situation of social media marketing,classical marketing researches can not be fully applied to describe the spreading of product’s information and consumers’ideas in the dynamic marketing network.Therefore,we have established a novel PHSU（Potential-Hesitant-Satisfied-Unsatisfied）model based on scale-free network to study the marketing dynamics of products.When the basic reproduction number R₀<1,the equilibrium of satisfied consumer disappearance is globally stable,and the consumers who are satisfied with the product will eventually disappear;when R₀>1,the equilibrium of satisfied consumer persistence is globally attractive,the product can be welcomed in the market,and regardless of the initial proportion of satisfied consumers in the population,the product information will eventually remain and spread on the social media marketing network.In addition,we also study the weighted model and analyze the corresponding dynamic behavior.Finally,we validate the above theory through simulations,and show the impact of heterogeneity of the network,people’s purchase intention and advertising intensity on social media marketing.（3）In order to analyze a kind of online fraud which is prevalent in China at present,we propose a novel SVFR（Susceptible-Victim-Fraudster-Resister）online fraud information spreading model based on the mean field theory to discuss the spreading process of this kind of fraud information on the online social networks in detail.The model takes into account the Scale-free property of the online social networks.Both fraudsters and victims will spread the fraud information,and the immigration of the population are also considered.Firstly,we calculate the threshold（basic reproduction number）that can predict the spread of network fraud,and study the global attractiveness of the equilibrium through a novel monotone iterative algorithm.Then,we give several methods to curb fraud,and compare their effects through simulation.Finally,by combining the survey data with the model,we make a further practical exploration.