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Dynamical systems analysis of a two-level trophic food web in the southern oceans


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Hadley, SA 2009 , 'Dynamical systems analysis of a two-level trophic food web in the southern oceans', Research Master thesis, University of Tasmania.

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A theoretical model developed by Stone describing a two level trophic system
in the Ocean is analysed, for the case in which there is unlimited supply of
nutrients. It is shown that spontaneous oscillations in population numbers are
possible, but they do not arise from a Hopf bifurcation. Seasonal forcing of the
model is also investigated, and it is shown that resonances can occur, in addition
to highly nonlinear behaviour including high period oscillations, quasi-periodicity
and chaos.
The model is then extended to include the case in which nutrient concentrations
are allowed to vary. In this model seasonal forcing is not considered.
Nevertheless a Hopf bifurcation is found for a critical value of the bifurcation
parameter which is chosen as the non-dimensional reproductive rate of bacteria.
The Hopf bifurcation gives rise to oscillatory solutions appearing as limit
cycles. The stability of the limit cycles found is determined using Floquet
theory, where it is observed that the periodic solutions arise from the Hopf
bifurcation as stable orbits. As the bifurcation parameter is varied the branch of
oscillatory solutions loses stability. This is due to a fold bifurcation, giving rise
to regions in the parameter space where two different oscillatory solutions are
possible for the same parameter values.

Item Type: Thesis - Research Master
Authors/Creators:Hadley, SA
Copyright Holders: The Author
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Copyright 2009 the Author - The University is continuing to endeavour to trace the copyright owner(s) and in the meantime this item has been reproduced here in good faith. We would be pleased to hear from the copyright owner(s).

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