Research On Rumor Spreading Model Of Rational Interaction In Social Networks

With the development of the Internet,people can instantly share information on social networks,but at the same time it also exacerbates rumor propagation.Studying the mechanism of rumor propagation is of great significance for understanding the law of rumor propagation and controlling the propagation of rumors.Individuals in social networks react differently to rumors.There is little research on the influence of a few rational people who do not blindly faith in rumors,and rational people are meaningful to suppress rumor spread.The rumor spreading model of rational interaction is established,considering group sharing of information,random disturbance,media influence and other mechanisms to analyze dynamics.The main content of this dissertation is as follows:Considering members of social network groups through group sharing and propagation during the spreading of rumors,a rumor spreading model considering group propagation and rational interaction on homogeneous networks and heterogeneous networks is developed.The differential dynamic method and the next generation matrix theory are exploited to calculate rumor free equilibrium and basic reproduction number of the model and the correctness of the model is verified.The dynamic changes of the ignorant,the rational and the spreader under real-world applications are simulated on the ER,WS,BA,and Facebook networks respectively.The simulation results show that when the rumors gradually disappear,the density of the ignorant and the rational in the four types of networks can be stabilized;and the rumor in the BA and Facebook networks spreads and disappears faster than that in the ER and WS networks.Theory and simulation analysis demonstrates that larger groups can enhance the influence range of rumor propagation and more credible rational people can significantly reduce the time and range of rumors propagation.The number of users changes dynamically in a social network,and the topology of the network is affected by external environmental noise,which is described as a standard Brownian motion,while stochastic differential equations have been derived to characterize the rumor propagation model of rational interaction on homogeneous networks with noise interference.Then,theoretical analysis on the homogeneous networks proves the existence and uniqueness of the global positive solutions of the model,provides sufficient conditions for the disappearance of rumors and verifies the correctness of the model.The simulation results on the WS network show that the more credible rational person significantly reduces the peak density of rumors.Weak noise can cause the peak density of spreaders to increase,the life cycle of rumors is reduced,and the phenomenon of stochastic resonance appears.On the basis of the rumor spreading model of rational interaction,we take the influence of positive and negative media reports on rumor dissemination into consideration,the rumor free equilibrium and basic reproduction number of the model are calculated,verifying the theoretical derivation.The results showed that positive media coverage can reduce the spread of rumors,whereas negative reports will expand the scope of the rumors spread.When the interaction rate of rational persons in the model is higher than that of communicators,it will significantly reduce the spread range and shorten the spreading time of rumors.Therefore,by improving the credibility of rational people and enhancing the positive influence of the media,the harm of the spread of rumors can be better suppressed.