Global Behavior for a Strongly Coupled Predator-Prey Model with One Resource and Two Consumers
We consider a strongly coupled predator-prey model with one resource and two consumers, in which the first consumer species feeds on the resource according to the Holling II functional response, while the second consumer species feeds on the resource following the Beddington-DeAngelis functional res...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/183285 |
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| _version_ | 1849695291463172096 |
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| author | Yujuan Jiao Shengmao Fu |
| author_facet | Yujuan Jiao Shengmao Fu |
| author_sort | Yujuan Jiao |
| collection | DOAJ |
| description | We consider a strongly coupled predator-prey model with one resource and two consumers, in which the first consumer species feeds on the resource according to the Holling II functional response, while the second consumer species feeds on the resource following the Beddington-DeAngelis functional response, and they compete for the common resource. Using the energy estimates and Gagliardo-Nirenberg-type inequalities, the existence and uniform boundedness of global solutions for the model are proved. Meanwhile, the sufficient conditions for global asymptotic stability of the positive equilibrium for this model are given by constructing a Lyapunov function. |
| format | Article |
| id | doaj-art-d6dd487858c84c3f9b81e8de87eed7c5 |
| institution | DOAJ |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-d6dd487858c84c3f9b81e8de87eed7c52025-08-20T03:19:49ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/183285183285Global Behavior for a Strongly Coupled Predator-Prey Model with One Resource and Two ConsumersYujuan Jiao0Shengmao Fu1College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, ChinaCollege of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, ChinaWe consider a strongly coupled predator-prey model with one resource and two consumers, in which the first consumer species feeds on the resource according to the Holling II functional response, while the second consumer species feeds on the resource following the Beddington-DeAngelis functional response, and they compete for the common resource. Using the energy estimates and Gagliardo-Nirenberg-type inequalities, the existence and uniform boundedness of global solutions for the model are proved. Meanwhile, the sufficient conditions for global asymptotic stability of the positive equilibrium for this model are given by constructing a Lyapunov function.http://dx.doi.org/10.1155/2012/183285 |
| spellingShingle | Yujuan Jiao Shengmao Fu Global Behavior for a Strongly Coupled Predator-Prey Model with One Resource and Two Consumers Abstract and Applied Analysis |
| title | Global Behavior for a Strongly Coupled Predator-Prey Model with One Resource and Two Consumers |
| title_full | Global Behavior for a Strongly Coupled Predator-Prey Model with One Resource and Two Consumers |
| title_fullStr | Global Behavior for a Strongly Coupled Predator-Prey Model with One Resource and Two Consumers |
| title_full_unstemmed | Global Behavior for a Strongly Coupled Predator-Prey Model with One Resource and Two Consumers |
| title_short | Global Behavior for a Strongly Coupled Predator-Prey Model with One Resource and Two Consumers |
| title_sort | global behavior for a strongly coupled predator prey model with one resource and two consumers |
| url | http://dx.doi.org/10.1155/2012/183285 |
| work_keys_str_mv | AT yujuanjiao globalbehaviorforastronglycoupledpredatorpreymodelwithoneresourceandtwoconsumers AT shengmaofu globalbehaviorforastronglycoupledpredatorpreymodelwithoneresourceandtwoconsumers |