Travelling waves in Lotka-Volterra competition models

In this thesis, we study a class of multi-stable reaction-diffusion systems used to model competing species. Systems in this class possess uniform stable steady states representing semi-trivial solutions. We start by considering a bistable, interaction, where the interactions are of classic “Lotka-Volterra” type and we consider a particular problem with relevance to applications in population dynamics: essentially, we study under what conditions the interplay of relative motility (diffusion) and competitive strength can cause waves of invasion to be halted and reversed. By establishing rigorous results concerning related degenerate and near-degenerate systems,we build a picture of the dependence of the wave speed on system parameters. Our results lead us to conjecture that this class of competition model has three “zones of response” in which the wave direction is left-moving, reversible and right-moving, respectively and indeed that in all three zones, the wave speed is an increasing function of the relative motility. Moreover, we study the effects of domain size on planar and non-planar interfaces and show that curvature plays an important role in determining competitive outcomes. Finally, we study a 3-species Lotka-Volterra model, where the third species is treated as a bio-control agent or a bio-buffer and investigate under what conditions the third species can alter the existing competition interaction.

Name dc:type.qualificationname

Doctor of Philosophy

Level dc:type.qualificationlevel

Doctoral Thesis

Grantor dc:publisher.institution

University of Dundee

Year dc:date.issued

2011

Author dc:creator

• Alzahrani, Ebraheem

Advisor dc:contributor.advisor

• Davidson, Fordyce

• Travelling waves
• Competition Lotka-Volterra models
• Bistable
• Tristable

Language dc:language

eng

Identifier

oai:discovery.dundee.ac.uk:studenttheses/1e432558-a3eb-40ee-81ae-4f0af74718d0

OAI identifier oai:identifier

oai:discovery.dundee.ac.uk:studenttheses/1e432558-a3eb-40ee-81ae-4f0af74718d0