N-Species Delay Lotka-Volterra Competition System With Random Perturbation

The study about mathematical biology become more and more important in the 21th century. The intersectant domain will be researched mainly between mathematical biology and other subjects. Compared with the determinate mathematical biology model, species ecology systems are often subject to environmental noise, it is important to discover whether the presence of a such noise affects these results that we have obtained.In this paper, we shall consider the existence,uniqueness,boundedness,persistence and global asymptotic stability of positive solutions to stochastic differential equations with finite delay.This paper is composed of two parts. In the first chapter, we introduce the historical background of the problems which will be investigated and the main results of this paper. Also , we will state some preminary results which will be used in our paper. In the second chapter, in Section 2.1, the existence and the uniqueness of positive solutions to equation are studied which is fundamental for the subsequent developments. In Section 2.2, we shall discuss the boundedness of positive solutions to equation . In Section 2.3, we devote to the study persistence. Finally, we shall proof that positive solutions to equation are global asymptotic stability in Section 2.4.