Dynamics of a Stage Structured Pest Control Model in a Polluted Environment with Pulse Pollution Input
By using pollution model and impulsive delay differential equation, we formulate a pest control model with stage structure for natural enemy in a polluted environment by introducing a constant periodic pollutant input and killing pest at different fixed moments and investigate the dynamics of such a...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/678762 |
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| _version_ | 1832567165676421120 |
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| author | Bing Liu Ling Xu Baolin Kang |
| author_facet | Bing Liu Ling Xu Baolin Kang |
| author_sort | Bing Liu |
| collection | DOAJ |
| description | By using pollution model and impulsive delay differential equation, we formulate a pest control model with stage structure for natural enemy in a polluted environment by introducing a constant periodic pollutant input and killing pest at different fixed moments and investigate the dynamics of such a system. We assume only that the natural enemies are affected by pollution, and we choose the method to kill the pest without harming natural enemies. Sufficient conditions for global attractivity of the natural enemy-extinction periodic solution and permanence of the system are obtained. Numerical simulations are presented to confirm our theoretical results. |
| format | Article |
| id | doaj-art-4136d028170a463ebb0d9b1dc22327a9 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-4136d028170a463ebb0d9b1dc22327a92025-02-03T01:02:11ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/678762678762Dynamics of a Stage Structured Pest Control Model in a Polluted Environment with Pulse Pollution InputBing Liu0Ling Xu1Baolin Kang2Department of Mathematics, Anshan Normal University, Anshan, Liaoning 114007, ChinaDepartment of Mathematics, Liaoning Normal University, Dalian, Liaoning 116029, ChinaDepartment of Mathematics, Anshan Normal University, Anshan, Liaoning 114007, ChinaBy using pollution model and impulsive delay differential equation, we formulate a pest control model with stage structure for natural enemy in a polluted environment by introducing a constant periodic pollutant input and killing pest at different fixed moments and investigate the dynamics of such a system. We assume only that the natural enemies are affected by pollution, and we choose the method to kill the pest without harming natural enemies. Sufficient conditions for global attractivity of the natural enemy-extinction periodic solution and permanence of the system are obtained. Numerical simulations are presented to confirm our theoretical results.http://dx.doi.org/10.1155/2013/678762 |
| spellingShingle | Bing Liu Ling Xu Baolin Kang Dynamics of a Stage Structured Pest Control Model in a Polluted Environment with Pulse Pollution Input Journal of Applied Mathematics |
| title | Dynamics of a Stage Structured Pest Control Model in a Polluted Environment with Pulse Pollution Input |
| title_full | Dynamics of a Stage Structured Pest Control Model in a Polluted Environment with Pulse Pollution Input |
| title_fullStr | Dynamics of a Stage Structured Pest Control Model in a Polluted Environment with Pulse Pollution Input |
| title_full_unstemmed | Dynamics of a Stage Structured Pest Control Model in a Polluted Environment with Pulse Pollution Input |
| title_short | Dynamics of a Stage Structured Pest Control Model in a Polluted Environment with Pulse Pollution Input |
| title_sort | dynamics of a stage structured pest control model in a polluted environment with pulse pollution input |
| url | http://dx.doi.org/10.1155/2013/678762 |
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