Dynamical Systems Analysis of a Five-Dimensional Trophic Food Web Model in the Southern Oceans
A theoretical model developed by Stone describing a three-level trophic system in the Ocean is analysed. The system consists of two distinct predator-prey networks, linked by competition for nutrients at the lowest level. There is also an interaction at the level of the two preys, in the sense that...
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2009/575047 |
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| _version_ | 1832551905559052288 |
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| author | Scott A. Hadley Lawrence K. Forbes |
| author_facet | Scott A. Hadley Lawrence K. Forbes |
| author_sort | Scott A. Hadley |
| collection | DOAJ |
| description | A theoretical model developed by Stone describing a three-level trophic system in the Ocean is analysed. The system consists of two distinct predator-prey networks, linked by competition for nutrients at the lowest level. There is also an interaction at the level of the two preys, in the sense that the presence of one is advantageous to the other when nutrients are low. It is shown that spontaneous oscillations in population numbers are possible, and that they result from a Hopf bifurcation. The limit cycles are analysed using Floquet theory and are found to change from stable to unstable as a solution branch is traversed. |
| format | Article |
| id | doaj-art-caaff500a0bf424bb34923a1a3da7c25 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-caaff500a0bf424bb34923a1a3da7c252025-02-03T06:00:18ZengWileyJournal of Applied Mathematics1110-757X1687-00422009-01-01200910.1155/2009/575047575047Dynamical Systems Analysis of a Five-Dimensional Trophic Food Web Model in the Southern OceansScott A. Hadley0Lawrence K. Forbes1Department of Defence, Anglesea Barracks, Hobart, Tasmania 7000, AustraliaSchool of Maths and Physics, University of Tasmania, Private Bag 37, Hobart, Tasmania 7001, AustraliaA theoretical model developed by Stone describing a three-level trophic system in the Ocean is analysed. The system consists of two distinct predator-prey networks, linked by competition for nutrients at the lowest level. There is also an interaction at the level of the two preys, in the sense that the presence of one is advantageous to the other when nutrients are low. It is shown that spontaneous oscillations in population numbers are possible, and that they result from a Hopf bifurcation. The limit cycles are analysed using Floquet theory and are found to change from stable to unstable as a solution branch is traversed.http://dx.doi.org/10.1155/2009/575047 |
| spellingShingle | Scott A. Hadley Lawrence K. Forbes Dynamical Systems Analysis of a Five-Dimensional Trophic Food Web Model in the Southern Oceans Journal of Applied Mathematics |
| title | Dynamical Systems Analysis of a Five-Dimensional Trophic Food Web Model in the Southern Oceans |
| title_full | Dynamical Systems Analysis of a Five-Dimensional Trophic Food Web Model in the Southern Oceans |
| title_fullStr | Dynamical Systems Analysis of a Five-Dimensional Trophic Food Web Model in the Southern Oceans |
| title_full_unstemmed | Dynamical Systems Analysis of a Five-Dimensional Trophic Food Web Model in the Southern Oceans |
| title_short | Dynamical Systems Analysis of a Five-Dimensional Trophic Food Web Model in the Southern Oceans |
| title_sort | dynamical systems analysis of a five dimensional trophic food web model in the southern oceans |
| url | http://dx.doi.org/10.1155/2009/575047 |
| work_keys_str_mv | AT scottahadley dynamicalsystemsanalysisofafivedimensionaltrophicfoodwebmodelinthesouthernoceans AT lawrencekforbes dynamicalsystemsanalysisofafivedimensionaltrophicfoodwebmodelinthesouthernoceans |