A Rosenzweig-MacArthur (1963) Criterion for the Chemostat
The Rosenzweig-MacArthur (1963) criterion is a graphical criterion that has been widely used for elucidating the local stability properties of the Gause (1934) type predator-prey systems. It has not been stated whether a similar criterion holds for models with explicit resource dynamics (Kooi et al....
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2016/5626980 |
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| _version_ | 1832558536629944320 |
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| author | Torsten Lindström Yuanji Cheng |
| author_facet | Torsten Lindström Yuanji Cheng |
| author_sort | Torsten Lindström |
| collection | DOAJ |
| description | The Rosenzweig-MacArthur (1963) criterion is a graphical criterion that has been widely used for elucidating the local stability properties of the Gause (1934) type predator-prey systems. It has not been stated whether a similar criterion holds for models with explicit resource dynamics (Kooi et al. (1998)), like the chemostat model. In this paper we use the implicit function theorem and implicit derivatives for proving that a similar graphical criterion holds under chemostat conditions, too. |
| format | Article |
| id | doaj-art-7470aee2550f44adb059d86e99c789bc |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-7470aee2550f44adb059d86e99c789bc2025-02-03T01:32:10ZengWileyThe Scientific World Journal2356-61401537-744X2016-01-01201610.1155/2016/56269805626980A Rosenzweig-MacArthur (1963) Criterion for the ChemostatTorsten Lindström0Yuanji Cheng1Department of Mathematics, Linnaeus University, 35195 Växjö, SwedenSchool of Technology, Malmö University, 20506 Malmö, SwedenThe Rosenzweig-MacArthur (1963) criterion is a graphical criterion that has been widely used for elucidating the local stability properties of the Gause (1934) type predator-prey systems. It has not been stated whether a similar criterion holds for models with explicit resource dynamics (Kooi et al. (1998)), like the chemostat model. In this paper we use the implicit function theorem and implicit derivatives for proving that a similar graphical criterion holds under chemostat conditions, too.http://dx.doi.org/10.1155/2016/5626980 |
| spellingShingle | Torsten Lindström Yuanji Cheng A Rosenzweig-MacArthur (1963) Criterion for the Chemostat The Scientific World Journal |
| title | A Rosenzweig-MacArthur (1963) Criterion for the Chemostat |
| title_full | A Rosenzweig-MacArthur (1963) Criterion for the Chemostat |
| title_fullStr | A Rosenzweig-MacArthur (1963) Criterion for the Chemostat |
| title_full_unstemmed | A Rosenzweig-MacArthur (1963) Criterion for the Chemostat |
| title_short | A Rosenzweig-MacArthur (1963) Criterion for the Chemostat |
| title_sort | rosenzweig macarthur 1963 criterion for the chemostat |
| url | http://dx.doi.org/10.1155/2016/5626980 |
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