Dynamic Analysis Of Network Information Propagation Models

The development of Internet technology has brought an unprecedented opportunity for the information era of industry,but it also brings trouble on the security of network information,which especially highlights in the security issues of wireless sensor networks and social networks.Because of the constrained resource,the wireless sensors with high-density deployment are mostly threatened by information stealing and destroying attacks launched by such malware as virus,worm,Troy horse and spy-ware.Social networks,due to its less constraints on the virtual crowds,have greatly weakened the determinacy and reliability of all kinds of information in the networks,and lead to all sorts of harmful information to widely burst.In view of this,this paper focuses on the theme of the dynamic analysis and control of network harmful information propagation models.The overall research ideas include:propose network harmful information propagation models;analyze the dynamic characteristics of network systems by using the theory of(partial)functional differential equations,such as Hopf bifurcation,periodic solutions,traveling wave solutions and so on;put forward reasonable control method,such as optimal control,network immune control and so on;form an comprehensive innovation system of theory and application.The research method of this paper is helpful to promote the innovation of the theory of network information spreading and provide an important theoretical guidance for the government to prevent and control harmful information.The main work of this paper includes the following aspects.1.Aiming at the problem of malware propagation in wireless sensor networks,we reveal the inherent law of malware propagation by establishing a delayed differential equation model.The Hopf bifurcation threshold is determined by taking a time delay as the bifurcation parameter.Applying the dimension reduction idea of center manifold theory,the direction and the stability of periodic solutions are discussed.Meanwhile,we creatively introduce the optimal control theory,and design an optimal controller in the process of rumor propagation.The research shows that the time delay can cause the stability switch phenomenon,and the application of an optimal controller can reduce the number of infected nodes in sensor networks with less control cost.2.Aiming at the influence of spatial mobility of the sensors on malware propagation in wireless sensor networks,we propose a new malware propagation model with consideration of spatial diffusion and time delay in a mobile wireless sensor network.The existence of non-negative solutions and the boundedness of the solutions are discussed.The sufficient conditions of network instability,which is caused by time delay,are obtianed by matrix eigenvalue analysis method.Applying the dimension reduction idea of center manifold theory,the direction and the stability of periodic solutions are analyzed.Numerical results have comprehensively analyzed the influence of time delay,receiving rate,communication radius and spatial diffusion on malware propagation.The research shows that the spatial mobility of the sensors can change the convergence speed of the model,and also enhance the amplitude of the model under unstable conditions.3.Aiming at the psychological response of users during rumor propagation in social networks,we propose a delayed rumor propagation model with consideration of Holling-type II saturated incidence and network topology.The existence of equilibrium points and the boundedness of the solutions are discussed.We have tackled tons of obstacles about stability analysis of high dimensional systems,and analyzed the local stability and global stability.Meanwhile,acccording to the network topology,network immune control and optimal control are designed.Numerical simulations have analyzed the comprehensive influence of time delay,degree,psychological reaction and optimal control on rumor propagation.The research shows that the better the psychological factor of individuals is,the lower the density of rumor infected individuals will be or even there will not exist any rumor infected individuals.4.Aiming at the problem of rumor spatiotemporal propagation,we have established a reactiondiffusion rumor propagation model in social networks.The local stability and global stability of the equilibrium points are discussed.By analyzing the existence of travelling wave solutions,the transition process of rumor propagation is given.Further,we study the Hopf bifurcation and stability switch by taking time delay as a bifurcation parameter.Finally,numerical simulations are performed to verify the theoretical analysis.The research shows that the critical speed of rumor propagation determines the final form of rumor propagation,and time delay is one of the important factors that causes network instability.5.Aiming at the spatial delayed response of rumor propagation in social networks,we propoese a reaction-diffusion rumor propagation model with a spatial-temporal delay term by using partial functional differential equations.Theoretical analysis is given to determine the stability and Hopf bifurcation of our model.The numerical results find that on the one hand,the spatial-temporal delay can change the stability of the system,on the other hand,the spatial-temporal delay can also delay the convergence time of the system.From the perspective of theory and simulation,this work puts forward a new viewpoint on the study of information propagation,and develops the existing theory of information propagation.