Dynamics of a stochastic predator–prey model with distributed delay and Markovian switching

Qun Liu; Daqing Jiang; Tasawar Hayat; Ahmed Alsaedi

doi:10.1016/j.physa.2019.121264

Dynamics of a stochastic predator–prey model with distributed delay and Markovian switching

Qun Liu
, Daqing Jiang
, Tasawar Hayat
, Ahmed Alsaedi

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

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

15 Scopus citations

Abstract

In this paper, we study a stochastic predator–prey model with distributed delay and Markovian switching. Firstly, we obtain sufficient criteria for weak persistence of the predator population. Then in the case of weak persistence, we establish sufficient conditions for the existence of positive recurrence of the solutions to the model by constructing a suitable stochastic Lyapunov function with regime switching. Finally, we establish sufficient conditions for extinction of the predator population.

Original language	English
Article number	121264
Journal	Physica A: Statistical Mechanics and its Applications
Volume	527
DOIs	https://doi.org/10.1016/j.physa.2019.121264
State	Published - 1 Aug 2019
Externally published	Yes

UN SDGs

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

SDG 15 Life on Land

Keywords

Distributed delay
Markovian switching
Positive recurrence and extinction
Stochastic predator–prey model
Weak persistence

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10.1016/j.physa.2019.121264

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title = "Dynamics of a stochastic predator–prey model with distributed delay and Markovian switching",

abstract = "In this paper, we study a stochastic predator–prey model with distributed delay and Markovian switching. Firstly, we obtain sufficient criteria for weak persistence of the predator population. Then in the case of weak persistence, we establish sufficient conditions for the existence of positive recurrence of the solutions to the model by constructing a suitable stochastic Lyapunov function with regime switching. Finally, we establish sufficient conditions for extinction of the predator population.",

keywords = "Distributed delay, Markovian switching, Positive recurrence and extinction, Stochastic predator–prey model, Weak persistence",

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AU - Hayat, Tasawar

AU - Alsaedi, Ahmed

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Y1 - 2019/8/1

N2 - In this paper, we study a stochastic predator–prey model with distributed delay and Markovian switching. Firstly, we obtain sufficient criteria for weak persistence of the predator population. Then in the case of weak persistence, we establish sufficient conditions for the existence of positive recurrence of the solutions to the model by constructing a suitable stochastic Lyapunov function with regime switching. Finally, we establish sufficient conditions for extinction of the predator population.

AB - In this paper, we study a stochastic predator–prey model with distributed delay and Markovian switching. Firstly, we obtain sufficient criteria for weak persistence of the predator population. Then in the case of weak persistence, we establish sufficient conditions for the existence of positive recurrence of the solutions to the model by constructing a suitable stochastic Lyapunov function with regime switching. Finally, we establish sufficient conditions for extinction of the predator population.

KW - Distributed delay

KW - Markovian switching

KW - Positive recurrence and extinction

KW - Stochastic predator–prey model

KW - Weak persistence

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ER -

Dynamics of a stochastic predator–prey model with distributed delay and Markovian switching

Abstract

UN SDGs

Keywords

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