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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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/973805 |
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| _version_ | 1849683600859987968 |
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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. |
| format | Article |
| id | doaj-art-d419caf50c0748d28832090cc4b038b2 |
| institution | DOAJ |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| 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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