The threshold of a chemostat model with single-species growth on two nutrients under telegraph noise

被引：9
|
作者：
Gao, Miaomiao [1 ]
Jiang, Daqing [1 ,2 ,3 ]
Hayat, Tasawar [3 ,4 ]
机构：
[1] China Univ Petr East China, Coll Sci, Qingdao 266580, Shandong, Peoples R China
[2] China Univ Petr East China, Key Lab Unconvent Oil & Gas Dev, Minist Educ, Qingdao 266580, Shandong, Peoples R China
[3] King Abdulaziz Univ, Dept Math, Nonlinear Anal & Appl Math NAAM Res Grp, Jeddah 21589, Saudi Arabia
[4] Quaid I Azam Univ, Dept Math, Islamabad 44000, Pakistan
来源：
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2019年 / 75卷
关键词：
Chemostat model; Telegraph noise; Extinction; Positive recurrence; BREAK-EVEN CONCENTRATION; COMPETITIVE-EXCLUSION; POPULATIONS; SYSTEMS;
D O I：
10.1016/j.cnsns.2019.03.027
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we investigate the dynamics of a chemostat model with single-species growth on two nutrients, which is disturbed by the telegraph noise. Switching between different environmental states is achieved by Markov chain. Firstly, we prove the existence and uniqueness of the positive solution. Then the threshold between extinction and persistence in the mean of the microorganism is obtained. Moreover, in the case of persistence, we establish sufficient conditions for the existence of positive recurrence. Finally, some simulations are carried out to demonstrate our theoretical results. Our main effort is to build the suitable Lyapunov functions with regime switching. (C) 2019 Elsevier B.V. All rights reserved.
引用
收藏
页码：160 / 173
页数：14
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