Threshold behavior of a stochastic Lotka–Volterra food chain chemostat model with jumps

Miaomiao Gao; Daqing Jiang; Tasawar Hayat; Ahmed Alsaedi

doi:10.1016/j.physa.2019.02.029

Threshold behavior of a stochastic Lotka–Volterra food chain chemostat model with jumps

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

16 Scopus citations

Abstract

Taking lévy jumps into account, a Lotka–Volterra food chain chemostat model in random environment is proposed and investigated. We first prove the existence and uniqueness of the global positive solution. Then conditions for extinction of the microorganisms are derived in two cases. Furthermore, we establish sufficient conditions for persistence in the mean of the system. Theoretical analysis indicates that the dynamics of the considered model are determined by two threshold parameters R₀ ^s and R₁ ^s, and both white noise and lévy noise are disadvantageous to the system. Finally, numerical simulations are given to illustrate the results.

Original language	English
Pages (from-to)	191-203
Number of pages	13
Journal	Physica A: Statistical Mechanics and its Applications
Volume	523
DOIs	https://doi.org/10.1016/j.physa.2019.02.029
State	Published - 1 Jun 2019
Externally published	Yes

Keywords

Extinction
Lévy jumps
Persistence in the mean
Stochastic food chain chemostat model
Threshold value

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10.1016/j.physa.2019.02.029

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title = "Threshold behavior of a stochastic Lotka–Volterra food chain chemostat model with jumps",

abstract = "Taking l{\'e}vy jumps into account, a Lotka–Volterra food chain chemostat model in random environment is proposed and investigated. We first prove the existence and uniqueness of the global positive solution. Then conditions for extinction of the microorganisms are derived in two cases. Furthermore, we establish sufficient conditions for persistence in the mean of the system. Theoretical analysis indicates that the dynamics of the considered model are determined by two threshold parameters R0 s and R1 s, and both white noise and l{\'e}vy noise are disadvantageous to the system. Finally, numerical simulations are given to illustrate the results.",

keywords = "Extinction, L{\'e}vy jumps, Persistence in the mean, Stochastic food chain chemostat model, Threshold value",

author = "Miaomiao Gao and Daqing Jiang and Tasawar Hayat and Ahmed Alsaedi",

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T1 - Threshold behavior of a stochastic Lotka–Volterra food chain chemostat model with jumps

AU - Gao, Miaomiao

AU - Jiang, Daqing

AU - Hayat, Tasawar

AU - Alsaedi, Ahmed

PY - 2019/6/1

Y1 - 2019/6/1

N2 - Taking lévy jumps into account, a Lotka–Volterra food chain chemostat model in random environment is proposed and investigated. We first prove the existence and uniqueness of the global positive solution. Then conditions for extinction of the microorganisms are derived in two cases. Furthermore, we establish sufficient conditions for persistence in the mean of the system. Theoretical analysis indicates that the dynamics of the considered model are determined by two threshold parameters R0 s and R1 s, and both white noise and lévy noise are disadvantageous to the system. Finally, numerical simulations are given to illustrate the results.

AB - Taking lévy jumps into account, a Lotka–Volterra food chain chemostat model in random environment is proposed and investigated. We first prove the existence and uniqueness of the global positive solution. Then conditions for extinction of the microorganisms are derived in two cases. Furthermore, we establish sufficient conditions for persistence in the mean of the system. Theoretical analysis indicates that the dynamics of the considered model are determined by two threshold parameters R0 s and R1 s, and both white noise and lévy noise are disadvantageous to the system. Finally, numerical simulations are given to illustrate the results.

KW - Extinction

KW - Lévy jumps

KW - Persistence in the mean

KW - Stochastic food chain chemostat model

KW - Threshold value

UR - https://www.scopus.com/pages/publications/85062152580

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DO - 10.1016/j.physa.2019.02.029

M3 - Article

AN - SCOPUS:85062152580

SN - 0378-4371

VL - 523

SP - 191

EP - 203

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

ER -

Threshold behavior of a stochastic Lotka–Volterra food chain chemostat model with jumps

Abstract

Keywords

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