Time Delayed Stage-Structured Predator-Prey Model with Birth Pulse and Pest Control Tactics
Normally, chemical pesticides kill not only pests but also their natural enemies. In order to better control the pests, two-time delayed stage-structured predator-prey models with birth pulse and pest control tactics are proposed and analyzed by using impulsive differential equations in present work...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/935923 |
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| _version_ | 1832555916070748160 |
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| author | Mei Yan Yongfeng Li Zhongyi Xiang |
| author_facet | Mei Yan Yongfeng Li Zhongyi Xiang |
| author_sort | Mei Yan |
| collection | DOAJ |
| description | Normally, chemical pesticides kill not only pests but also their natural enemies. In order to better control the pests, two-time delayed stage-structured predator-prey models with birth pulse and pest control tactics are proposed and analyzed by using impulsive differential equations in present work. The stability threshold conditions for the mature prey-eradication periodic solutions of two models are derived, respectively. The effects of key parameters including killing efficiency rate, pulse period, the maximum birth effort per unit of time of natural enemy, and maturation time of prey on the threshold values are discussed in more detail. By comparing the two threshold values of mature prey-extinction, we provide the fact that the second control tactic is more effective than the first control method. |
| format | Article |
| id | doaj-art-3ea7125519b94efaa95698cd83eedfd7 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-3ea7125519b94efaa95698cd83eedfd72025-02-03T05:46:52ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/935923935923Time Delayed Stage-Structured Predator-Prey Model with Birth Pulse and Pest Control TacticsMei Yan0Yongfeng Li1Zhongyi Xiang2Key Laboratory of Biologic Resources Protection and Utilization of Hubei Province, Enshi, Hubei 445000, ChinaDepartment of Mathematics and Information Sciences, Zhengzhou University of Light Industry, Zhengzhou, Henan 450002, ChinaKey Laboratory of Biologic Resources Protection and Utilization of Hubei Province, Enshi, Hubei 445000, ChinaNormally, chemical pesticides kill not only pests but also their natural enemies. In order to better control the pests, two-time delayed stage-structured predator-prey models with birth pulse and pest control tactics are proposed and analyzed by using impulsive differential equations in present work. The stability threshold conditions for the mature prey-eradication periodic solutions of two models are derived, respectively. The effects of key parameters including killing efficiency rate, pulse period, the maximum birth effort per unit of time of natural enemy, and maturation time of prey on the threshold values are discussed in more detail. By comparing the two threshold values of mature prey-extinction, we provide the fact that the second control tactic is more effective than the first control method.http://dx.doi.org/10.1155/2014/935923 |
| spellingShingle | Mei Yan Yongfeng Li Zhongyi Xiang Time Delayed Stage-Structured Predator-Prey Model with Birth Pulse and Pest Control Tactics Abstract and Applied Analysis |
| title | Time Delayed Stage-Structured Predator-Prey Model with Birth Pulse and Pest Control Tactics |
| title_full | Time Delayed Stage-Structured Predator-Prey Model with Birth Pulse and Pest Control Tactics |
| title_fullStr | Time Delayed Stage-Structured Predator-Prey Model with Birth Pulse and Pest Control Tactics |
| title_full_unstemmed | Time Delayed Stage-Structured Predator-Prey Model with Birth Pulse and Pest Control Tactics |
| title_short | Time Delayed Stage-Structured Predator-Prey Model with Birth Pulse and Pest Control Tactics |
| title_sort | time delayed stage structured predator prey model with birth pulse and pest control tactics |
| url | http://dx.doi.org/10.1155/2014/935923 |
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