Dynamical behavior of stochastic predator-prey models with distributed delay and general functional response

Qun Liu; Daqing Jiang; Tasawar Hayat; Ahmed Alsaedi

doi:10.1080/07362994.2019.1695628

Dynamical behavior of stochastic predator-prey models with distributed delay and general functional response

Qun Liu
, Daqing Jiang
, Tasawar Hayat
, Ahmed Alsaedi

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

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

9 Scopus citations

Abstract

In this article, we study two stochastic predator-prey models with distributed delay and general functional response. For the nonautonomous periodic case of the system, by utilizing Khasminskii’s theory of periodic solution, we prove that the system admits a positive T-periodic solution. For the system which is perturbed by both white and colored noises, we establish sufficient conditions for the existence of positive recurrence of the solutions to the system. The existence of positive recurrence implies stochastic weak stability.

Original language	English
Pages (from-to)	403-426
Number of pages	24
Journal	Stochastic Analysis and Applications
Volume	38
Issue number	3
DOIs	https://doi.org/10.1080/07362994.2019.1695628
State	Published - 3 May 2020
Externally published	Yes

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SDG 15 Life on Land

Keywords

Stochastic predator-prey model
distributed delay
general functional response
periodic solution
positive recurrence

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10.1080/07362994.2019.1695628

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title = "Dynamical behavior of stochastic predator-prey models with distributed delay and general functional response",

abstract = "In this article, we study two stochastic predator-prey models with distributed delay and general functional response. For the nonautonomous periodic case of the system, by utilizing Khasminskii{\textquoteright}s theory of periodic solution, we prove that the system admits a positive T-periodic solution. For the system which is perturbed by both white and colored noises, we establish sufficient conditions for the existence of positive recurrence of the solutions to the system. The existence of positive recurrence implies stochastic weak stability.",

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

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T1 - Dynamical behavior of stochastic predator-prey models with distributed delay and general functional response

AU - Liu, Qun

AU - Jiang, Daqing

AU - Hayat, Tasawar

AU - Alsaedi, Ahmed

PY - 2020/5/3

Y1 - 2020/5/3

N2 - In this article, we study two stochastic predator-prey models with distributed delay and general functional response. For the nonautonomous periodic case of the system, by utilizing Khasminskii’s theory of periodic solution, we prove that the system admits a positive T-periodic solution. For the system which is perturbed by both white and colored noises, we establish sufficient conditions for the existence of positive recurrence of the solutions to the system. The existence of positive recurrence implies stochastic weak stability.

AB - In this article, we study two stochastic predator-prey models with distributed delay and general functional response. For the nonautonomous periodic case of the system, by utilizing Khasminskii’s theory of periodic solution, we prove that the system admits a positive T-periodic solution. For the system which is perturbed by both white and colored noises, we establish sufficient conditions for the existence of positive recurrence of the solutions to the system. The existence of positive recurrence implies stochastic weak stability.

KW - Stochastic predator-prey model

KW - distributed delay

KW - general functional response

KW - periodic solution

KW - positive recurrence

UR - https://www.scopus.com/pages/publications/85075529033

U2 - 10.1080/07362994.2019.1695628

DO - 10.1080/07362994.2019.1695628

M3 - Article

AN - SCOPUS:85075529033

SN - 0736-2994

VL - 38

SP - 403

EP - 426

JO - Stochastic Analysis and Applications

JF - Stochastic Analysis and Applications

IS - 3

ER -

Dynamical behavior of stochastic predator-prey models with distributed delay and general functional response

Abstract

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Keywords

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