Stochastic Dynamics Analysis Of Predation Model And Rumor Propagation Model

In this paper,the stochastic dynamic behavior of the predator-prey model and the rumor propagation model are discussed respectively.For the predator-prey model with Bddington-DeAngelis function response function,considering the influence of the natural environment and the population structure on the population,the Allee effect is introduced into the bait equation,and the Brown movement and the population mean two random parameters are added in the model.The only positive global solution of the model is obtained by using the Ito formula and the Lyapunov functional,then the index of the global solution of the model is also discussed.The condition of stability is obtained.For the rumor propagation model,considering the effect of noise and time,Brown movement is introduced into the model,and the model coefficient is a function of time.At least one T periodic solution is obtained by using the Lyapunov functional method.