Multi-State Dependent Impulsive Control for Holling I Predator-Prey Model
According to the different effects of biological and chemical control, we propose a model for Holling I functional response predator-prey system concerning pest control which adopts different control methods at different thresholds. By using differential equation geometry theory and the method of su...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2012/181752 |
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| _version_ | 1832567212928401408 |
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| author | Huidong Cheng Fang Wang Tongqian Zhang |
| author_facet | Huidong Cheng Fang Wang Tongqian Zhang |
| author_sort | Huidong Cheng |
| collection | DOAJ |
| description | According to the different effects of biological and chemical control, we propose a model for Holling I functional response predator-prey system concerning pest control which adopts different control methods at different thresholds. By using differential equation geometry theory and the method of successor functions, we prove that the existence of order one periodic solution of such system and the attractiveness of the order one periodic solution by sequence convergence rules and qualitative analysis. Numerical simulations are carried out to illustrate the feasibility of our main results which show that our method used in this paper is more efficient and easier than the existing ones for proving the existence of order one periodic solution. |
| format | Article |
| id | doaj-art-077601859eb64b628442f769953f3ea0 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-077601859eb64b628442f769953f3ea02025-02-03T01:02:00ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2012-01-01201210.1155/2012/181752181752Multi-State Dependent Impulsive Control for Holling I Predator-Prey ModelHuidong Cheng0Fang Wang1Tongqian Zhang2College of Science, Shandong University of Science and Technology, Qingdao 266510, ChinaCollege of Science, Shandong University of Science and Technology, Qingdao 266510, ChinaCollege of Science, Shandong University of Science and Technology, Qingdao 266510, ChinaAccording to the different effects of biological and chemical control, we propose a model for Holling I functional response predator-prey system concerning pest control which adopts different control methods at different thresholds. By using differential equation geometry theory and the method of successor functions, we prove that the existence of order one periodic solution of such system and the attractiveness of the order one periodic solution by sequence convergence rules and qualitative analysis. Numerical simulations are carried out to illustrate the feasibility of our main results which show that our method used in this paper is more efficient and easier than the existing ones for proving the existence of order one periodic solution.http://dx.doi.org/10.1155/2012/181752 |
| spellingShingle | Huidong Cheng Fang Wang Tongqian Zhang Multi-State Dependent Impulsive Control for Holling I Predator-Prey Model Discrete Dynamics in Nature and Society |
| title | Multi-State Dependent Impulsive Control for Holling I Predator-Prey Model |
| title_full | Multi-State Dependent Impulsive Control for Holling I Predator-Prey Model |
| title_fullStr | Multi-State Dependent Impulsive Control for Holling I Predator-Prey Model |
| title_full_unstemmed | Multi-State Dependent Impulsive Control for Holling I Predator-Prey Model |
| title_short | Multi-State Dependent Impulsive Control for Holling I Predator-Prey Model |
| title_sort | multi state dependent impulsive control for holling i predator prey model |
| url | http://dx.doi.org/10.1155/2012/181752 |
| work_keys_str_mv | AT huidongcheng multistatedependentimpulsivecontrolforhollingipredatorpreymodel AT fangwang multistatedependentimpulsivecontrolforhollingipredatorpreymodel AT tongqianzhang multistatedependentimpulsivecontrolforhollingipredatorpreymodel |