Dynamic Behavior Of A Stochastic Three-group Predator Model With Reciprocity Of Prey

In recent years,deterministic mathematical models have been widely used in the field of biomathematics research,and has always played a dominant role.How-ever,in the natural environment,the biological population is inevitably affected by the random factors of the external environment.Therefore,building the stochastic mathematical model to characterize the dynamics of the population in a random environment,has become a major research topic in modern biological mathematic-s.Based on this,we mainly studies the dynamical properties of a class of stochastic three populations model with prey mutualism in this paper.Firstly,under some appropriate assumptions,by means of several important definitions,lemmas and theorems,the survival analysis of the model is carried out,and sufficient criteria of the persistence and the extinction of each population for the model are established.Secondly,by constructing the Lyapunov function,using Hasminskii stationary distribution theory,it is proved that there is a stationary distribution to this model and it has the ergodic property,which indicates that the average of time for the population tends to the stationary distribution with proba-bility.Furthermore,the global asymptotic stability of this model is studied.Finally,several numerical simulation are carried out with Matlab to verify and supplement the validity of the results in this paper.