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

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• 作者：Shulin Sun^a ; ^{sunshulin2013@163.com} ; Yaru Sun^a ; Guang Zhang ; ^b ; ^{lxyzhg@tjcu.edu.cn} ; Xinzhi Liu^c
• 关键词：Stochastic chemostat model ; Mean reverting process ; It&ocirc ; &rsquo ; s formula ; Asymptotic behavior ; Stationary distribution
• 刊名：Applied Mathematics and Computation
• 出版年：2017
• 出版时间：1 April 2017
• 年：2017
• 卷：298
• 期：Complete
• 页码：153-170
• 全文大小：624 K
• 卷排序：298

文摘

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 Itô’s formula, Lyaponov method and Gronwall inequality. In addition, numerical simulations are given to illustrate the theoretical results.