Journal of Applied Mathematics

Dynamical Systems Analysis of a Five-Dimensional Trophic Food Web Model in the Southern Oceans

Scott A. Hadley and Lawrence K. Forbes

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Abstract

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.

Article information

Source
J. Appl. Math., Volume 2009 (2009), Article ID 575047, 17 pages.

Dates
First available in Project Euclid: 2 March 2010

Permanent link to this document
https://projecteuclid.org/euclid.jam/1267538757

Digital Object Identifier
doi:10.1155/2009/575047

Zentralblatt MATH identifier
1196.37125

Citation

Hadley, Scott A.; Forbes, Lawrence K. Dynamical Systems Analysis of a Five-Dimensional Trophic Food Web Model in the Southern Oceans. J. Appl. Math. 2009 (2009), Article ID 575047, 17 pages. doi:10.1155/2009/575047. https://projecteuclid.org/euclid.jam/1267538757


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