Journal of Applied Mathematics
Volume 2009 (2009), Article ID 575047, 17 pages
Research Article

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

1Department of Defence, Anglesea Barracks, Hobart, Tasmania 7000, Australia
2School of Maths and Physics, University of Tasmania, Private Bag 37, Hobart, Tasmania 7001, Australia

Received 4 May 2009; Accepted 19 November 2009

Academic Editor: Patrick De Leenheer

Copyright © 2009 Scott A. Hadley and Lawrence K. Forbes. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.