Periodic Solution for a Stochastic Non-autonomous Predator-Prey Model with Holling II Functional Response

Li Zu; Daqing Jiang; Donal O’Regan

doi:10.1007/s10440-018-0205-y

Periodic Solution for a Stochastic Non-autonomous Predator-Prey Model with Holling II Functional Response

Li Zu
, Daqing Jiang
, Donal O’Regan

Mathematics

Hainan Normal University
China University of Petroleum (East China)
King Abdulaziz University

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

13 Citations (Scopus)

Abstract

A biological population may be subjected to stochastic disturbance and exhibit periodicity. In this paper, a stochastic non-autonomous predator-prey system with Holling II functional response is proposed, and the existence of a unique positive solution is derived. We give sufficient conditions for extinction and strong persistence in the mean by analyzing a corresponding one-dimensional stochastic system. Also we establish the existence of positive periodic solutions for this stochastic non-autonomous predator-prey system. Finally, we use numerical simulations to illustrate our results and we present some conclusions and future directions. The results of this paper provide methods for other stochastic population models, which we hope to analyze in the future.

Original language	English
Pages (from-to)	89-105
Number of pages	17
Journal	Acta Applicandae Mathematicae
Volume	161
Issue number	1
DOIs	https://doi.org/10.1007/s10440-018-0205-y
Publication status	Published - 1 Jun 2019

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SDG 15 Life on Land

Keywords

Holling II functional response
Non-autonomous
Periodic solution
Stochastic predator-prey system

Authors (Note for portal: view the doc link for the full list of authors)

Authors
Zu, L;Jiang, DQ;O'Regan, D

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10.1007/s10440-018-0205-y

Cite this

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abstract = "A biological population may be subjected to stochastic disturbance and exhibit periodicity. In this paper, a stochastic non-autonomous predator-prey system with Holling II functional response is proposed, and the existence of a unique positive solution is derived. We give sufficient conditions for extinction and strong persistence in the mean by analyzing a corresponding one-dimensional stochastic system. Also we establish the existence of positive periodic solutions for this stochastic non-autonomous predator-prey system. Finally, we use numerical simulations to illustrate our results and we present some conclusions and future directions. The results of this paper provide methods for other stochastic population models, which we hope to analyze in the future.",

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AU - Zu, Li

AU - Jiang, Daqing

AU - O’Regan, Donal

PY - 2019/6/1

Y1 - 2019/6/1

N2 - A biological population may be subjected to stochastic disturbance and exhibit periodicity. In this paper, a stochastic non-autonomous predator-prey system with Holling II functional response is proposed, and the existence of a unique positive solution is derived. We give sufficient conditions for extinction and strong persistence in the mean by analyzing a corresponding one-dimensional stochastic system. Also we establish the existence of positive periodic solutions for this stochastic non-autonomous predator-prey system. Finally, we use numerical simulations to illustrate our results and we present some conclusions and future directions. The results of this paper provide methods for other stochastic population models, which we hope to analyze in the future.

AB - A biological population may be subjected to stochastic disturbance and exhibit periodicity. In this paper, a stochastic non-autonomous predator-prey system with Holling II functional response is proposed, and the existence of a unique positive solution is derived. We give sufficient conditions for extinction and strong persistence in the mean by analyzing a corresponding one-dimensional stochastic system. Also we establish the existence of positive periodic solutions for this stochastic non-autonomous predator-prey system. Finally, we use numerical simulations to illustrate our results and we present some conclusions and future directions. The results of this paper provide methods for other stochastic population models, which we hope to analyze in the future.

KW - Holling II functional response

KW - Non-autonomous

KW - Periodic solution

KW - Stochastic predator-prey system

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JO - Acta Applicandae Mathematicae

JF - Acta Applicandae Mathematicae

IS - 1

ER -

Periodic Solution for a Stochastic Non-autonomous Predator-Prey Model with Holling II Functional Response

Abstract

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Keywords

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