Stochastic Dynamics Analysis Of Rumor Propagation Model

In the era of rapid development of the Internet,the influence of rumor propagation is increasingly serious.The establishment of rumor propagation model and the effective control of rumor propagation have become an urgent problem for all kinds of experts and scholars.However,the classical SI rumor propagation model ignores the influence of random fluctuation of the system's external environment on the rumor propagation rate,In order to establish a more perfect rumor propagation model,this paper embeds this factor into the classical rumor propagation model and establishes a rumor propagation model with Markov switching.The threshold dynamics and ergodicity of the improved rumor propagation model are studied by using the stochastic differential equation and the stability theory of Markov process.The main contents of this paper are as follows:Firstly,the classic SI(Sensitive users-infected user)model is improved by adding the in-fluence of random fluctuations of the system's external environment on the rumor propagation rate,and a rumor propagation model with Markov switch is established.Secondly,the thresh-old of rumor extinction and persistence is obtained.Then,it is proved that there is an invariant probability measure in the case of rumor persistence,and at the same time,under relatively weak conditions,the solution's ?-limit set and attractor are obtained;Finally,the global con-vergence of the total variation norm from the instantaneous transition probability measure to the invariant measure is proved.