Research On Network Propagation Dynamics And Optimal Control Application

Information dissemination has always been one of the most important propagation phenomena in human society.With the globalization of the Internet,the Internet has become the main media of information dissemination.In recent years,online applications such as online social networks have become very popular.As a result,the amount of information and the speed of information dissemination has increased greatly,which has significantly increased the impact of various information dissemination phenomena on society.Therefore,it is of great significance to study the process of information dissemination on the Internet.Using the method of network propagation dynamics and optimal control,this paper analyzed two typical and similar information transmission phenomena: rumor spreading and word-of-mouth marketing.Rumor propagationRumors can spread rapidly through the Internet and bring serious adverse effects to the society.When a rumor appears and spreads on the Internet,publishing the truth to the crowd is an effective way to alleviate the negative impact caused by the rumor.This paper focuses on the problem of finding a cost-effective anti-rumor message-pushing scheme.First,this paper proposes a novel node-level rumor spreading model with anti-rumor message-pushing mechanism.Based on this model,the cost effectiveness of an anti-rumor message-pushing scheme is estimated and thereby the original problem is modeled as an optimal control problem.Then we derive the optimality system for the optimal control problem.Finally,we show the performance of the control obtained from the optimality system and the influences of the propagation parameters.Word-of-mouth marketingWith the widespread application of social media,word-of-mouth marketing has become one of the most effective marketing methods.This paper is devoted to designing an effective dynamic discount pricing strategy in competitive marketing with consideration of the word-of-mouth propagation.First,we introduce a competitive word-of-mouth propagation model with dynamic discount pricing mechanism.On this basis,we quantify the benefits that each dynamic discount pricing strategy can bring to the merchant and model the original problem as an optimal control problem.Next,we derive the optimality system for the optimal control problem and,thereby propose the concept of competitive dynamic discount pricing strategy.Through comparative experiments,we find that the profit of the competitive dynamic discount pricing strategy is satisfactory.Finally,we show the impact of propagation parameters.Our findings contribute to maximizing the marketing profit in the presence of commercial competitors.