Dynamical Analysis Of Rumor Spreading Model With Impulse Effort And Delay Effort

In the internet era,rumor spreading has broken through geographical restrictions,the spread of rumor is more easily.It can spread throughout the world in a very short time.Those rumors not only cause social panic,but also bring social mass incidents.Therefore,the research on revealing the mechanism of rumor spread and proposing the reasonable effective control measures is of great significance to our society.The occurrence of time delay can lead to changes of the dynamic properties of the model,even change the stability of the system.In the process of rumor spreading,one chooses whether to spread under a thinking and identifying time after knows the rumor,the time is defined as delay.Similarly,official information plays a great role in controlling rumor,it is not so timely and often has a lag effect.Besides,the voice of the government is not continuous,but discontinuous,which fit impulse behavior.In this paper,we consider a more complex dynamical system with time delay and impulse effect,and we describe the law and characteristics of rumor spreading in the new period,which has important theoretical and guiding significance to control the spread of rumors.The contents include the following three parts:(1)We propose a rumor spreading model with impulse vaccination and time delay,by using the Floquet theory of impulsive equation and comparison theorem,we obtained two key thresholds which can be used to determine the rumor dynamics process.We also showed that a short impulse period,a large impulse vaccination rate or a long latent period is sufficient condition for the disappearance of rumors.(2)We build an optimal control of rumor spreading model with delay.To prevent the spread of rumor,we introduce two control strategies to minimize both the number of ignorant,spreader and the cost of two strategies.By using Pontryagin'5 maximum principle,a necessary condition for optimal control strategies has been derived.We proved that the spreading of rumor can be controlled most effectively by using the two strategies together.(3)We build an interaction evolution model between the public and official opinion fields in network mass incidents with two delays.We use the central manifold theorem and the normal form method to study the direction and stability of bifurcation periodic solutions.Our model indicates that there exists a golden time for government intervention,which should be emphasized given the impact of modern media and inaccurate rumors.In this paper,we introduced time delay effect and impulse effect,and improved the existing theory of rumor spreading.The results of the study showed that we couldn't overlook the role of time delay in rumor spreading,if misses the moment,it will take a high price to eliminate negative public opinion in the latter.What's more,we studied the influence of scientific knowledge and official information on rumor spreading,the relevant research conclusions can be used as the decision support for the government to deal with the spread of rumor.