Mathematical modelling of mutualism in population ecology

Hdl Handle:
http://hdl.handle.net/10034/345676
Title:
Mathematical modelling of mutualism in population ecology
Authors:
Rowntree, Andrew
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.
Advisors:
Kavallaris, Nikos I.; Roberts, Jason A.
Publisher:
University of Chester
Publication Date:
Sep-2014
URI:
http://hdl.handle.net/10034/345676
Type:
Thesis or dissertation
Language:
en
Appears in Collections:
Masters Dissertations

Full metadata record

DC FieldValue Language
dc.contributor.advisorKavallaris, Nikos I.en
dc.contributor.advisorRoberts, Jason A.en
dc.contributor.authorRowntree, Andrewen
dc.date.accessioned2015-02-27T14:47:17Zen
dc.date.available2015-02-27T14:47:17Zen
dc.date.issued2014-09en
dc.identifier.urihttp://hdl.handle.net/10034/345676en
dc.description.abstractThis 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.en
dc.language.isoenen
dc.publisherUniversity of Chesteren
dc.subjectmathematical modellingen
dc.subjectpopulation ecologyen
dc.titleMathematical modelling of mutualism in population ecologyen
dc.typeThesis or dissertationen
dc.type.qualificationnameMScen
dc.type.qualificationlevelMasters Degreeen
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