Periodic Solution of Prey-Predator Model with Beddington-DeAngelis Functional Response and Impulsive State Feedback Control
A prey-predator model with Beddington-DeAngelis functional response and impulsive state feedback control is investigated. We obtain the sufficient conditions of the global asymptotical stability of the system without impulsive effects. By using the geometry theory of semicontinuous dynamic system an...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/607105 |
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| _version_ | 1832555985337581568 |
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| author | Chunjin Wei Lansun Chen |
| author_facet | Chunjin Wei Lansun Chen |
| author_sort | Chunjin Wei |
| collection | DOAJ |
| description | A prey-predator model with Beddington-DeAngelis functional response and impulsive state feedback control is investigated. We obtain the sufficient conditions of the global asymptotical stability of the system without impulsive effects. By using the geometry theory of semicontinuous dynamic system and the method of successor function, we obtain the system with impulsive effects that has an order one periodic solution, and sufficient conditions for existence and stability of order one periodic solution are also obtained. Finally, numerical simulations are performed to illustrate our main results. |
| format | Article |
| id | doaj-art-45cf3279892e401d8c252fbcc0ca5b39 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-45cf3279892e401d8c252fbcc0ca5b392025-02-03T05:46:38ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/607105607105Periodic Solution of Prey-Predator Model with Beddington-DeAngelis Functional Response and Impulsive State Feedback ControlChunjin Wei0Lansun Chen1Science College, Jimei University, Fujian, Xiamen 361021, ChinaAcademy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, ChinaA prey-predator model with Beddington-DeAngelis functional response and impulsive state feedback control is investigated. We obtain the sufficient conditions of the global asymptotical stability of the system without impulsive effects. By using the geometry theory of semicontinuous dynamic system and the method of successor function, we obtain the system with impulsive effects that has an order one periodic solution, and sufficient conditions for existence and stability of order one periodic solution are also obtained. Finally, numerical simulations are performed to illustrate our main results.http://dx.doi.org/10.1155/2012/607105 |
| spellingShingle | Chunjin Wei Lansun Chen Periodic Solution of Prey-Predator Model with Beddington-DeAngelis Functional Response and Impulsive State Feedback Control Journal of Applied Mathematics |
| title | Periodic Solution of Prey-Predator Model with Beddington-DeAngelis Functional Response and Impulsive State Feedback Control |
| title_full | Periodic Solution of Prey-Predator Model with Beddington-DeAngelis Functional Response and Impulsive State Feedback Control |
| title_fullStr | Periodic Solution of Prey-Predator Model with Beddington-DeAngelis Functional Response and Impulsive State Feedback Control |
| title_full_unstemmed | Periodic Solution of Prey-Predator Model with Beddington-DeAngelis Functional Response and Impulsive State Feedback Control |
| title_short | Periodic Solution of Prey-Predator Model with Beddington-DeAngelis Functional Response and Impulsive State Feedback Control |
| title_sort | periodic solution of prey predator model with beddington deangelis functional response and impulsive state feedback control |
| url | http://dx.doi.org/10.1155/2012/607105 |
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