Using Transfer Function Analysis in Modelling Biological Invasions
Dreiwi, Hanan
Date: 22 June 2012
Thesis or dissertation
Publisher
University of Exeter
Degree Title
PhD in Mathematics
Abstract
This thesis is made up of seven chapters and two appendices. Chapter 1
provides an introduction whilst Chapter 7 o ers a conclusion. In Chapter 2 we
provide preliminaries on population projection models and robustness analysis.
In Chapter 3 we introduce a stage-structured model in a context of biological
invasions. Using a Transfer ...
This thesis is made up of seven chapters and two appendices. Chapter 1
provides an introduction whilst Chapter 7 o ers a conclusion. In Chapter 2 we
provide preliminaries on population projection models and robustness analysis.
In Chapter 3 we introduce a stage-structured model in a context of biological
invasions. Using a Transfer Function Approach, we provide a detailed analysis
of the invasion model where the existence and local stability of all possible
equilibria are characterised in terms of the underlying parameters of the model.
In Chapter 4, a Lyapunov function approach is used to estimate the basin of
attraction for each equilibrium. In Chapter 5, harvesting is incorporated into
the model and we speci cally examine the e ect of harvesting on whether
one or both of the species are eliminated. In Chapter 6 we introduce a novel
technique to measure the possibility of invasion in non-normal systems where
the traditional invasion exponent technique is unreliable.
Doctoral Theses
Doctoral College
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