Stationary distribution of a stochastic predator–prey model with distributed delay and general functional response

Qun Liu; Daqing Jiang; Xiuli He; Tasawar Hayat; Ahmed Alsaedi

doi:10.1016/j.physa.2018.09.033

Stationary distribution of a stochastic predator–prey model with distributed delay and general functional response

Qun Liu
, Daqing Jiang
, Xiuli He
, Tasawar Hayat
, Ahmed Alsaedi

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

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

5 Scopus citations

Abstract

In this paper, we study a stochastic predator–prey model with distributed delay and general functional response. We transform the model with weak kernel case into an equivalent system through the linear chain technique. Since the diffusion matrix is degenerate, the uniform ellipticity condition does not hold. The Markov semigroup theory is used to derive the existence of a unique stable stationary distribution. We verify the densities of the distributions of the positive solutions can converge in L¹ to an invariant density.

Original language	English
Pages (from-to)	273-287
Number of pages	15
Journal	Physica A: Statistical Mechanics and its Applications
Volume	513
DOIs	https://doi.org/10.1016/j.physa.2018.09.033
State	Published - 1 Jan 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
General functional response
Markov semigroups
Stationary distribution
Stochastic predator–prey model

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10.1016/j.physa.2018.09.033

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abstract = "In this paper, we study a stochastic predator–prey model with distributed delay and general functional response. We transform the model with weak kernel case into an equivalent system through the linear chain technique. Since the diffusion matrix is degenerate, the uniform ellipticity condition does not hold. The Markov semigroup theory is used to derive the existence of a unique stable stationary distribution. We verify the densities of the distributions of the positive solutions can converge in L1 to an invariant density.",

keywords = "Distributed delay, General functional response, Markov semigroups, Stationary distribution, Stochastic predator–prey model",

author = "Qun Liu and Daqing Jiang and Xiuli He and Tasawar Hayat and Ahmed Alsaedi",

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AU - Liu, Qun

AU - Jiang, Daqing

AU - He, Xiuli

AU - Hayat, Tasawar

AU - Alsaedi, Ahmed

PY - 2019/1/1

Y1 - 2019/1/1

N2 - In this paper, we study a stochastic predator–prey model with distributed delay and general functional response. We transform the model with weak kernel case into an equivalent system through the linear chain technique. Since the diffusion matrix is degenerate, the uniform ellipticity condition does not hold. The Markov semigroup theory is used to derive the existence of a unique stable stationary distribution. We verify the densities of the distributions of the positive solutions can converge in L1 to an invariant density.

AB - In this paper, we study a stochastic predator–prey model with distributed delay and general functional response. We transform the model with weak kernel case into an equivalent system through the linear chain technique. Since the diffusion matrix is degenerate, the uniform ellipticity condition does not hold. The Markov semigroup theory is used to derive the existence of a unique stable stationary distribution. We verify the densities of the distributions of the positive solutions can converge in L1 to an invariant density.

KW - Distributed delay

KW - General functional response

KW - Markov semigroups

KW - Stationary distribution

KW - Stochastic predator–prey model

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JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

ER -

Stationary distribution of a stochastic predator–prey model with distributed delay and general functional response

Abstract

UN SDGs

Keywords

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