Dynamical behavior of a stochastic two-species Monod competition chemostat model

被引：51

作者：

Sun, Shulin ^{[1
]}

Sun, Yaru ^{[1
]}

Zhang, Guang ^{[2
]}

Liu, Xinzhi ^{[3
]}

机构：

[1] Shanxi Normal Univ, Sch Math & Comp Sci, Linfen 041004, Peoples R China

[2] Tianjin Univ Commerce, Sch Sci, Tianjin 300134, Peoples R China

[3] Univ Waterloo, Dept Appl Math, Waterloo, ON N2L 3G1, Canada

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2017年 / 298卷

基金：

中国国家自然科学基金;

关键词：

Stochastic chemostat model; Mean reverting process; Ito's formula; Asymptotic behavior; Stationary distribution; BREAK-EVEN CONCENTRATION; STATIONARY DISTRIBUTION; POPULATION SYSTEMS; EPIDEMIC MODEL; VARIABLE YIELD; PERTURBATION; EXTINCTION;

D O I：

10.1016/j.amc.2016.11.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper studies a stochastic two -species Monod competition chemostat model which is subject to environment noises. Such noises are described by independent standard Brownian motions. It proves that the initial value problem of the model has a unique positive global solution. However, unlike the corresponding deterministic model, the stochastic model no longer has positive equilibrium points. The asymptotic behaviors and the steady state distributions are established by using Ito's formula, Lyaponov method and Gronwall inequality. In addition, numerical simulations are given to illustrate the theoretical results. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：153 / 170

页数：18

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