Analysis of a Periodic Impulsive Predator-Prey System with Disease in the Prey
We investigate a periodic predator-prey system subject to impulsive perturbations, in which a disease can be transmitted among the prey species only, in this paper. With the help of the theory of impulsive differential equations and Lyapunov functional method, sufficient conditions for the permanenc...
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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/10.1155/2013/656920 |
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| _version_ | 1850225361066917888 |
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| author | Lianwen Wang Zhijun Liu |
| author_facet | Lianwen Wang Zhijun Liu |
| author_sort | Lianwen Wang |
| collection | DOAJ |
| description | We investigate a periodic predator-prey system subject to impulsive perturbations, in which a disease can be transmitted among the prey species only, in this paper. With the help of the theory of impulsive differential equations and Lyapunov functional method, sufficient conditions for the permanence, global attractivity, and partial extinction of system are established, respectively. It is shown that impulsive perturbations contribute to the above dynamics of the system. Numerical simulations are presented to substantiate the analytical results. |
| format | Article |
| id | doaj-art-587c1553e7c544038ecb8efd3dbda85c |
| institution | OA Journals |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-587c1553e7c544038ecb8efd3dbda85c2025-08-20T02:05:23ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/656920656920Analysis of a Periodic Impulsive Predator-Prey System with Disease in the PreyLianwen Wang0Zhijun Liu1Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000, ChinaDepartment of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000, ChinaWe investigate a periodic predator-prey system subject to impulsive perturbations, in which a disease can be transmitted among the prey species only, in this paper. With the help of the theory of impulsive differential equations and Lyapunov functional method, sufficient conditions for the permanence, global attractivity, and partial extinction of system are established, respectively. It is shown that impulsive perturbations contribute to the above dynamics of the system. Numerical simulations are presented to substantiate the analytical results.http://dx.doi.org/10.1155/2013/656920 |
| spellingShingle | Lianwen Wang Zhijun Liu Analysis of a Periodic Impulsive Predator-Prey System with Disease in the Prey Journal of Applied Mathematics |
| title | Analysis of a Periodic Impulsive Predator-Prey System with Disease in the Prey |
| title_full | Analysis of a Periodic Impulsive Predator-Prey System with Disease in the Prey |
| title_fullStr | Analysis of a Periodic Impulsive Predator-Prey System with Disease in the Prey |
| title_full_unstemmed | Analysis of a Periodic Impulsive Predator-Prey System with Disease in the Prey |
| title_short | Analysis of a Periodic Impulsive Predator-Prey System with Disease in the Prey |
| title_sort | analysis of a periodic impulsive predator prey system with disease in the prey |
| url | http://dx.doi.org/10.1155/2013/656920 |
| work_keys_str_mv | AT lianwenwang analysisofaperiodicimpulsivepredatorpreysystemwithdiseaseintheprey AT zhijunliu analysisofaperiodicimpulsivepredatorpreysystemwithdiseaseintheprey |