Asymmetrical Impact of Allee Effect on a Discrete-Time Predator-Prey System

A discrete-time predator-prey model is proposed with Leslie-type numerical response, and the asymmetrical influence of Allee effect on the proposed system is investigated. By mathematical analysis, locally stable conditions for the equilibrium points of the considered systems with or without Allee e...

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Main Authors: Wenting Wang, Yujuan Jiao, Xiuping Chen
Format: Article
Language:English
Published: Wiley 2013-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2013/973805
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author Wenting Wang
Yujuan Jiao
Xiuping Chen
author_facet Wenting Wang
Yujuan Jiao
Xiuping Chen
author_sort Wenting Wang
collection DOAJ
description A discrete-time predator-prey model is proposed with Leslie-type numerical response, and the asymmetrical influence of Allee effect on the proposed system is investigated. By mathematical analysis, locally stable conditions for the equilibrium points of the considered systems with or without Allee effect are obtained firstly. Furthermore, numerical simulation is used to verify the results and detect some new outcomes. The results show that Allee effect on predator leads the system to its stable state in much longer time. Conversely, the prey population with Allee effect makes it much faster. In particular, a large value of Allee effect on prey results in periodic dynamics of the system.
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publishDate 2013-01-01
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series Journal of Applied Mathematics
spelling doaj-art-d419caf50c0748d28832090cc4b038b22025-08-20T03:23:47ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/973805973805Asymmetrical Impact of Allee Effect on a Discrete-Time Predator-Prey SystemWenting Wang0Yujuan Jiao1Xiuping Chen2School of Mathematics and Computer Science, Northwest University for Nationalities, Lanzhou 730030, ChinaSchool of Mathematics and Computer Science, Northwest University for Nationalities, Lanzhou 730030, ChinaSchool of Mathematics and Computer Science, Northwest University for Nationalities, Lanzhou 730030, ChinaA discrete-time predator-prey model is proposed with Leslie-type numerical response, and the asymmetrical influence of Allee effect on the proposed system is investigated. By mathematical analysis, locally stable conditions for the equilibrium points of the considered systems with or without Allee effect are obtained firstly. Furthermore, numerical simulation is used to verify the results and detect some new outcomes. The results show that Allee effect on predator leads the system to its stable state in much longer time. Conversely, the prey population with Allee effect makes it much faster. In particular, a large value of Allee effect on prey results in periodic dynamics of the system.http://dx.doi.org/10.1155/2013/973805
spellingShingle Wenting Wang
Yujuan Jiao
Xiuping Chen
Asymmetrical Impact of Allee Effect on a Discrete-Time Predator-Prey System
Journal of Applied Mathematics
title Asymmetrical Impact of Allee Effect on a Discrete-Time Predator-Prey System
title_full Asymmetrical Impact of Allee Effect on a Discrete-Time Predator-Prey System
title_fullStr Asymmetrical Impact of Allee Effect on a Discrete-Time Predator-Prey System
title_full_unstemmed Asymmetrical Impact of Allee Effect on a Discrete-Time Predator-Prey System
title_short Asymmetrical Impact of Allee Effect on a Discrete-Time Predator-Prey System
title_sort asymmetrical impact of allee effect on a discrete time predator prey system
url http://dx.doi.org/10.1155/2013/973805
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AT yujuanjiao asymmetricalimpactofalleeeffectonadiscretetimepredatorpreysystem
AT xiupingchen asymmetricalimpactofalleeeffectonadiscretetimepredatorpreysystem