Stochastic Dynamics Analysis Of Cooperative Predation Model With Time Delay

In stochastic model,the stability in distribution of solutions is a question which is impor-tant and challenging,researchers often study it by finding the positive equilibrium state.This paper is mainly studying a three-species model with time delays in which one species feeds on two other cooperative species.The traditional ways have some conditions or properties which is difficult to find or nonexistent for the delay model.The way we used in this paper can be used to study the delay model.First,considering the stochastic perturbations,we use Ito’s formula to deal with the model.Second,we set a criteria of the stability in distribution for each species xi(t)in the model,and study the extinction or existence of species by the given assumption condition and the relationship among species that we need to study.Finally,we obtain the dis-tribution of the solution of the three-species model is stable and weakly converges to a unique ergodic invariant distribution while the given assumption condition holds.