Positive Solutions for a General Gause-Type Predator-Prey Model with Monotonic Functional Response
We study a general Gause-type predator-prey model with monotonic functional response under Dirichlet boundary condition. Necessary and sufficient conditions for the existence and nonexistence of positive solutions for this system are obtained by means of the fixed point index theory. In addition, th...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/547060 |
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| _version_ | 1832561444054368256 |
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| author | Guohong Zhang Xiaoli Wang |
| author_facet | Guohong Zhang Xiaoli Wang |
| author_sort | Guohong Zhang |
| collection | DOAJ |
| description | We study a general Gause-type predator-prey model with
monotonic functional response under Dirichlet boundary condition. Necessary and
sufficient conditions for the existence and nonexistence of positive solutions for this
system are obtained by means of the fixed point index theory. In addition, the local
and global bifurcations from a semitrivial state are also investigated on the basis of
bifurcation theory. The results indicate diffusion, and functional response does help
to create stationary pattern. |
| format | Article |
| id | doaj-art-9d01e7252e9a4d4bb0e103a32efb3247 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-9d01e7252e9a4d4bb0e103a32efb32472025-02-03T01:25:06ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/547060547060Positive Solutions for a General Gause-Type Predator-Prey Model with Monotonic Functional ResponseGuohong Zhang0Xiaoli Wang1School of Mathematics and Statistics, Southwest University, Chongqing 400715, ChinaSchool of Mathematics and Statistics, Southwest University, Chongqing 400715, ChinaWe study a general Gause-type predator-prey model with monotonic functional response under Dirichlet boundary condition. Necessary and sufficient conditions for the existence and nonexistence of positive solutions for this system are obtained by means of the fixed point index theory. In addition, the local and global bifurcations from a semitrivial state are also investigated on the basis of bifurcation theory. The results indicate diffusion, and functional response does help to create stationary pattern.http://dx.doi.org/10.1155/2011/547060 |
| spellingShingle | Guohong Zhang Xiaoli Wang Positive Solutions for a General Gause-Type Predator-Prey Model with Monotonic Functional Response Abstract and Applied Analysis |
| title | Positive Solutions for a General Gause-Type Predator-Prey Model with Monotonic Functional Response |
| title_full | Positive Solutions for a General Gause-Type Predator-Prey Model with Monotonic Functional Response |
| title_fullStr | Positive Solutions for a General Gause-Type Predator-Prey Model with Monotonic Functional Response |
| title_full_unstemmed | Positive Solutions for a General Gause-Type Predator-Prey Model with Monotonic Functional Response |
| title_short | Positive Solutions for a General Gause-Type Predator-Prey Model with Monotonic Functional Response |
| title_sort | positive solutions for a general gause type predator prey model with monotonic functional response |
| url | http://dx.doi.org/10.1155/2011/547060 |
| work_keys_str_mv | AT guohongzhang positivesolutionsforageneralgausetypepredatorpreymodelwithmonotonicfunctionalresponse AT xiaoliwang positivesolutionsforageneralgausetypepredatorpreymodelwithmonotonicfunctionalresponse |