Research On The Problem Of Stochastic Persistence And Mean-square Stability Of Two Kinds Of Stochastic Population Models

The persistence and stability of the determine biological population model, al-ready have a lot of people studied. However, only a few people study the persistence and stability of the stochastic population model. And the definition of persistence of stochastic population model, can’t find the determine upper and lower bounds of the solutions of the model.Based on the question, we put forward a new definition of stochastic permanence, find two determine stochastic process, as upper and lower bounds of the solutions of the model. In this article, we study the stochastic persistence and mean square stability of the two kinds of biological stochastic population model, and using Ito formula, inverse transform and the orbit of the Brownian motion of the properties, we study the stochastic persistence of the stochastic Lotka-Volterra competitive model and stochastic delay Predator-Prey model. As well as using Ito formula, logarithmic transform and the differential mean value theorem, we get the mean square stability of the stochastic Lotka-Volterra competitive model and stochastic Predator-Prey model.This article main results and research methods play an important role and have some reference and application value for the later study of the stochastic persistence and the mean square stability.