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Mathematical modelling of mutualism in population ecology
Rowntree, Andrew P.
Rowntree, Andrew P.
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2014-09
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dissertation
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Abstract
This research dissertation focuses on the symbiotic interaction of mutualism, we give explanations as to what it is before mathematically modelling population dynamics of two species displaying mutualistic behaviour. Throughout the course of this dissertation, we
shall be re-examining the work done in the book by Kot [16] and the paper by Joharjee and Roberts [32], whilst providing further explanations of the mathematics involved and
the steps taken. We begin by constructing a model for mutualism before attempting to improve the model in order to make it more realistic. We go on to add delays to our improved
model and determine the stability of its equilibrium points. We formulate models via piecewise constant arguments and via a simple Euler scheme before determining stability for both systems. A graphical comparison will then be made to explain the differences in behaviour between the two discretised systems.
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University of Chester
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Thesis or dissertation
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en