Qualitative Analysis for a Predator Prey System with Holling Type III Functional Response and Prey Refuge
A predator prey system with Holling III functional response and constant prey refuge is considered. By using the Dulac criterion, we discuss the global stability of the positive equilibrium of the system. By transforming the system to a Liénard system, the conditions for the existence of exactly one...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2012/678957 |
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| _version_ | 1832562283958501376 |
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| author | Xia Liu Yepeng Xing |
| author_facet | Xia Liu Yepeng Xing |
| author_sort | Xia Liu |
| collection | DOAJ |
| description | A predator prey system with Holling III functional response and constant prey refuge is considered. By using the Dulac criterion, we discuss the global stability of the positive equilibrium of the system. By transforming the system to a Liénard system, the conditions for the existence of exactly one limit cycle for the system are given. Some numerical simulations are presented. |
| format | Article |
| id | doaj-art-c105ec748e124387a417802bd1562d60 |
| 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-c105ec748e124387a417802bd1562d602025-02-03T01:23:05ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2012-01-01201210.1155/2012/678957678957Qualitative Analysis for a Predator Prey System with Holling Type III Functional Response and Prey RefugeXia Liu0Yepeng Xing1College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, ChinaCollege of Mathematics and Science, Shanghai Normal University, Shanghai 200234, ChinaA predator prey system with Holling III functional response and constant prey refuge is considered. By using the Dulac criterion, we discuss the global stability of the positive equilibrium of the system. By transforming the system to a Liénard system, the conditions for the existence of exactly one limit cycle for the system are given. Some numerical simulations are presented.http://dx.doi.org/10.1155/2012/678957 |
| spellingShingle | Xia Liu Yepeng Xing Qualitative Analysis for a Predator Prey System with Holling Type III Functional Response and Prey Refuge Discrete Dynamics in Nature and Society |
| title | Qualitative Analysis for a Predator Prey System with Holling Type III Functional Response and Prey Refuge |
| title_full | Qualitative Analysis for a Predator Prey System with Holling Type III Functional Response and Prey Refuge |
| title_fullStr | Qualitative Analysis for a Predator Prey System with Holling Type III Functional Response and Prey Refuge |
| title_full_unstemmed | Qualitative Analysis for a Predator Prey System with Holling Type III Functional Response and Prey Refuge |
| title_short | Qualitative Analysis for a Predator Prey System with Holling Type III Functional Response and Prey Refuge |
| title_sort | qualitative analysis for a predator prey system with holling type iii functional response and prey refuge |
| url | http://dx.doi.org/10.1155/2012/678957 |
| work_keys_str_mv | AT xialiu qualitativeanalysisforapredatorpreysystemwithhollingtypeiiifunctionalresponseandpreyrefuge AT yepengxing qualitativeanalysisforapredatorpreysystemwithhollingtypeiiifunctionalresponseandpreyrefuge |