Boundedness and Global Stability for a Predator-Prey System with the Beddington-DeAngelis Functional Response
We study the qualitative behavior of a class of predator-prey models with Beddington-DeAngelis-type functional response, primarily from the viewpoint of permanence (uniform persistence). The Beddington-DeAngelis functional response is similar to the Holling type-II functional response but contains a...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Differential Equations and Nonlinear Mechanics |
| Online Access: | http://dx.doi.org/10.1155/2010/813289 |
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| _version_ | 1849685431155687424 |
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| author | Wahiba Khellaf Nasreddine Hamri |
| author_facet | Wahiba Khellaf Nasreddine Hamri |
| author_sort | Wahiba Khellaf |
| collection | DOAJ |
| description | We study the qualitative behavior of a class of predator-prey models with Beddington-DeAngelis-type functional response, primarily from the viewpoint of permanence (uniform persistence). The Beddington-DeAngelis functional response is similar to the Holling type-II functional response but contains a term describing mutual interference by predators. We establish criteria under which we have boundedness of solutions, existence of an attracting set, and global stability of the coexisting interior equilibrium via Lyapunov function. |
| format | Article |
| id | doaj-art-bf7b0eab6ee1448abd480866068b42f7 |
| institution | DOAJ |
| issn | 1687-4099 1687-4102 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Differential Equations and Nonlinear Mechanics |
| spelling | doaj-art-bf7b0eab6ee1448abd480866068b42f72025-08-20T03:23:08ZengWileyDifferential Equations and Nonlinear Mechanics1687-40991687-41022010-01-01201010.1155/2010/813289813289Boundedness and Global Stability for a Predator-Prey System with the Beddington-DeAngelis Functional ResponseWahiba Khellaf0Nasreddine Hamri1Laboratory of LMPA, University of Jijel, BP 98, Ouled Aissa, 18000 Jijel, AlgeriaLaboratory Math, University of Mentouri, 25000 Constantine, AlgeriaWe study the qualitative behavior of a class of predator-prey models with Beddington-DeAngelis-type functional response, primarily from the viewpoint of permanence (uniform persistence). The Beddington-DeAngelis functional response is similar to the Holling type-II functional response but contains a term describing mutual interference by predators. We establish criteria under which we have boundedness of solutions, existence of an attracting set, and global stability of the coexisting interior equilibrium via Lyapunov function.http://dx.doi.org/10.1155/2010/813289 |
| spellingShingle | Wahiba Khellaf Nasreddine Hamri Boundedness and Global Stability for a Predator-Prey System with the Beddington-DeAngelis Functional Response Differential Equations and Nonlinear Mechanics |
| title | Boundedness and Global Stability for a Predator-Prey System with the Beddington-DeAngelis Functional Response |
| title_full | Boundedness and Global Stability for a Predator-Prey System with the Beddington-DeAngelis Functional Response |
| title_fullStr | Boundedness and Global Stability for a Predator-Prey System with the Beddington-DeAngelis Functional Response |
| title_full_unstemmed | Boundedness and Global Stability for a Predator-Prey System with the Beddington-DeAngelis Functional Response |
| title_short | Boundedness and Global Stability for a Predator-Prey System with the Beddington-DeAngelis Functional Response |
| title_sort | boundedness and global stability for a predator prey system with the beddington deangelis functional response |
| url | http://dx.doi.org/10.1155/2010/813289 |
| work_keys_str_mv | AT wahibakhellaf boundednessandglobalstabilityforapredatorpreysystemwiththebeddingtondeangelisfunctionalresponse AT nasreddinehamri boundednessandglobalstabilityforapredatorpreysystemwiththebeddingtondeangelisfunctionalresponse |