Spreading Dynamic Analysis Of Social Information On Scale-free Networks

In recent years,with the rapid development of network information technology,the rise of online social networking platforms,such as Facebook,Twitter and Sina Weibo,makes it easier for people to access information.How to accurately reveal the law of information spreading in social networks and how to effectively affect and control the information spreading have become a hot topic in the field of complex network science,so the research of complex network has aroused the interest of many researchers.Complex network has been involved in many different fields,such as mathematical science,network topology theory,system science and spreading dynamics.Based on this,from the two perspectives of network topology and spreading dynamics,and then considering that scale-free network can more vividly reflect the real-world social network,this paper establishes the relevant model of social information spreading based on scale-free network.The model is studied and analyzed in detail.The work and innovation of this paper mainly include the following aspects:1. Considering the heterogeneity of social networks and the impact of information issuing and forwarding mechanism on social information dissemination,a new SIFT?Susceptible-Issuer-Forwarder-Stifler?social information spreading model is proposed based on scale-free networks.Based on the mean field theory,the basic reproductive numberR₀ of SIFT model and the equilibrium point of the system?including information-elimination equilibrium and information-prevailing equilibrium?are calculated.Then,the globally asymptotic stability,the persistence of information spreading and the global attractivity of information-prevailing equilibrium are studied in detail.2. Considering the influence of people's psychological factors?such as hesitation,forgetting,etc.?on rumor propagation,a new kind of SHPRS?Susceptible-hesitating-propagating-resisted?rumor propagation dynamic model is established based on scale-free network,and it is studied in detail.By means of the mean field theory,the basic reproductive number ₀R and equilibrium point of the model are calculated.Then,the globally asymptotic stability of rumor-free equilibrium and the global attractivity of the rumor-prevailing equilibrium are proved.The research shows that people's psychological changes do have an impact on rumor spreading.Further,some effective methods to control rumor spreading are given.3. Considering the influence of network heterogeneity,advertising attractivity and time delay,a new kind of advertising information spreading model with time delay based on the scale-free network is established,and the influence of advertising attractivity and time delay on advertising spreading is studied in detail.Through mathematical calculation,the basic reproductive number ₀R and equilibrium point are obtained.Then,the stability of the system is studied in detail.The globally asymptotic stability of the advertisement-free equilibrium and the global attractivity of the advertisement-prevailing equilibrium are proved.