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

被引：11

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

页码：160 / 173

页数：14

共 35 条

[1] On the basic reproduction number in a random environment [J].

Bacaer, Nicolas ;

Khaladi, Mohamed .

JOURNAL OF MATHEMATICAL BIOLOGY, 2013, 67 (6-7) :1729-1739

[2] Global analysis of competition for perfectly substitutable resources with linear response [J].

Ballyk, MM ;

McCluskey, CC ;

Wolkowicz, GSK .

JOURNAL OF MATHEMATICAL BIOLOGY, 2005, 51 (04) :458-490

[3]

BALLYK MM, 1995, J MATH BIOL, V33, P435

[4] A MATHEMATICAL-MODEL OF THE CHEMOSTAT WITH PERIODIC WASHOUT RATE [J].

BUTLER, GJ ;

HSU, SB ;

WALTMAN, P .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1985, 45 (03) :435-449

[5] Synchronization Control of Coupled Memristor-Based Neural Networks with Mixed Delays and Stochastic Perturbations [J].

Chen, Chuan ;

Li, Lixiang ;

Peng, Haipeng ;

Yang, Yixian ;

Li, Tao .

NEURAL PROCESSING LETTERS, 2018, 47 (02) :679-696

[6] Existence of stationary distributions for Kolmogorov systems of competitive type under telegraph noise [J].

Dang, N. H. ;

Du, N. H. ;

Yin, G. .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2014, 257 (06) :2078-2101

[7] An algorithmic introduction to numerical simulation of stochastic differential equations [J].

Higham, DJ .

SIAM REVIEW, 2001, 43 (03) :525-546

[8] Multigroup SIR epidemic model with stochastic perturbation [J].

Ji, Chunyan ;

Jiang, Daqing ;

Shi, Ningzhong .

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2011, 390 (10) :1747-1762

[9] COEXISTENCE OF 3 COMPETING MICROBIAL-POPULATIONS IN A CHEMOSTAT WITH PERIODICALLY VARYING DILUTION RATE [J].

LENAS, P ;

PAVLOU, S .

MATHEMATICAL BIOSCIENCES, 1995, 129 (02) :111-142

[10] COMPETITION BETWEEN 2 SPECIES FOR 2 COMPLEMENTARY OR SUBSTITUTABLE RESOURCES [J].

LEON, JA ;

TUMPSON, DB .

JOURNAL OF THEORETICAL BIOLOGY, 1975, 50 (01) :185-201

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