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.
['Scott Hadley', 'Lawrence K. Forbes']
Dynamical Systems Analysis of a Five-Dimensional Trophic Food Web Model in the Southern Oceans