Asymptotic Behavior Of Two Stochastic Ecological Mathematical Models

This dissertation is concerned with two stochastic ecologic mathematical models, which is composed of three parts as follows.We briefly introduce the recent development of stochastic differential equations. Some relevant definitions, theorems, important inequalities used in this article and the main results are given in the chapter 1.Chapter 2 deals with the asymptotic behavior of solutions for a stochastic Predator-Prey system where all a(t), b(t), c(t), d(t), f(t), m(t) are bounded and positive continuous functions. By suing moment estimation and inequality technique, the existence and uniqueness, random ultimate boundedness and random persistence of positive solutions of the equation (1), are obtained.In the chapter 3, the system of stochastic differential equations of Lotka-Volterra type dx(t)=diag(x1(t),…,xn(t))[a+Bx(t)+Cx(t-τ)dt+σx(t)dw(t)] (2) is considered, whereσ= (τij)n×n。The existence, uniqueness and random ultimate boundedness of solutions of the equation (2) are constructed by using Ito formula, moment estimation and inequality technique.