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

Miaomiao Gao; Daqing Jiang; Tasawar Hayat

doi:10.1016/j.cnsns.2019.03.027

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

Miaomiao Gao
, Daqing Jiang
, Tasawar Hayat

China University of Petroleum (East China)
King Abdulaziz University
Quaid-I-Azam University

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	160-173
Number of pages	14
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	75
DOIs	https://doi.org/10.1016/j.cnsns.2019.03.027
State	Published - Aug 2019
Externally published	Yes

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 15 Life on Land

Keywords

Chemostat model
Extinction
Positive recurrence
Telegraph noise

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10.1016/j.cnsns.2019.03.027

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

abstract = "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.",

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T1 - The threshold of a chemostat model with single-species growth on two nutrients under telegraph noise

AU - Gao, Miaomiao

AU - Jiang, Daqing

AU - Hayat, Tasawar

PY - 2019/8

Y1 - 2019/8

N2 - 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.

AB - 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.

KW - Chemostat model

KW - Extinction

KW - Positive recurrence

KW - Telegraph noise

UR - https://www.scopus.com/pages/publications/85063735169

U2 - 10.1016/j.cnsns.2019.03.027

DO - 10.1016/j.cnsns.2019.03.027

M3 - Article

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SN - 1007-5704

VL - 75

SP - 160

EP - 173

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

ER -

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

Abstract

UN SDGs

Keywords

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