Dynamical Analysis of a Stochastic Delayed Two-Species Competition Chemostat Model

In this paper, we consider a stochastic delayed two-species competition chemostat model with the Monod growth response function. First, we verify that there is a unique global positive solution for any given initial conditions for this stochastic delayed system. Second, we give the dynamical behavior of the solution of stochastic delay system around the washout equilibrium of deterministic system; moreover, we discuss the competition exclusion and coexistence of microorganisms x1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_1$$\end{document} and x2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_2$$\end{document}. Finally, computer simulations are carried out to illustrate the obtained results; in addition, results show that time delay has critical effects on the survival of the microorganisms.