Stationary distribution and extinction for a food chain chemostat model with random perturbation

Miaomiao Gao; Daqing Jiang; Tasawar Hayat; Ahmed Alsaedi

doi:10.1002/mma.6809

Stationary distribution and extinction for a food chain chemostat model with random perturbation

Miaomiao Gao
, Daqing Jiang
, Tasawar Hayat
, Ahmed Alsaedi

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

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

8 Scopus citations

Abstract

In this paper, we study the dynamical behavior of a stochastic food chain chemostat model, in which the white noise is proportional to the variables. Firstly, we prove the existence and uniqueness of the global positive solution. Then by constructing suitable Lyapunov functions, we show the system has a unique ergodic stationary distribution. Furthermore, the extinction of microorganisms is discussed in two cases. In one case, both the prey and the predator species are extinct, and in the other case, the prey species is surviving and the predator species is extinct. Finally, numerical experiments are performed for supporting the theoretical results.

Original language	English
Pages (from-to)	1013-1028
Number of pages	16
Journal	Mathematical Methods in the Applied Sciences
Volume	44
Issue number	1
DOIs	https://doi.org/10.1002/mma.6809
State	Published - 15 Jan 2021
Externally published	Yes

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

SDG 15 Life on Land

Keywords

Lyapunov function
extinction
stationary distribution
stochastic food chain chemostat model

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10.1002/mma.6809

Cite this

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title = "Stationary distribution and extinction for a food chain chemostat model with random perturbation",

abstract = "In this paper, we study the dynamical behavior of a stochastic food chain chemostat model, in which the white noise is proportional to the variables. Firstly, we prove the existence and uniqueness of the global positive solution. Then by constructing suitable Lyapunov functions, we show the system has a unique ergodic stationary distribution. Furthermore, the extinction of microorganisms is discussed in two cases. In one case, both the prey and the predator species are extinct, and in the other case, the prey species is surviving and the predator species is extinct. Finally, numerical experiments are performed for supporting the theoretical results.",

keywords = "Lyapunov function, extinction, stationary distribution, stochastic food chain chemostat model",

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T1 - Stationary distribution and extinction for a food chain chemostat model with random perturbation

AU - Gao, Miaomiao

AU - Jiang, Daqing

AU - Hayat, Tasawar

AU - Alsaedi, Ahmed

PY - 2021/1/15

Y1 - 2021/1/15

N2 - In this paper, we study the dynamical behavior of a stochastic food chain chemostat model, in which the white noise is proportional to the variables. Firstly, we prove the existence and uniqueness of the global positive solution. Then by constructing suitable Lyapunov functions, we show the system has a unique ergodic stationary distribution. Furthermore, the extinction of microorganisms is discussed in two cases. In one case, both the prey and the predator species are extinct, and in the other case, the prey species is surviving and the predator species is extinct. Finally, numerical experiments are performed for supporting the theoretical results.

AB - In this paper, we study the dynamical behavior of a stochastic food chain chemostat model, in which the white noise is proportional to the variables. Firstly, we prove the existence and uniqueness of the global positive solution. Then by constructing suitable Lyapunov functions, we show the system has a unique ergodic stationary distribution. Furthermore, the extinction of microorganisms is discussed in two cases. In one case, both the prey and the predator species are extinct, and in the other case, the prey species is surviving and the predator species is extinct. Finally, numerical experiments are performed for supporting the theoretical results.

KW - Lyapunov function

KW - extinction

KW - stationary distribution

KW - stochastic food chain chemostat model

UR - https://www.scopus.com/pages/publications/85090168785

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DO - 10.1002/mma.6809

M3 - Article

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SN - 0170-4214

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JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

IS - 1

ER -

Stationary distribution and extinction for a food chain chemostat model with random perturbation

Abstract

UN SDGs

Keywords

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