Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.505166
Title: Patterns in a Predator-PreyReaction-Diffusion System withNonlocal Effects
Author: Robertson, Nicholas
Awarding Body: University of Surrey
Current Institution: University of Surrey
Date of Award: 2008
Availability of Full Text:
Access through EThOS:
Abstract:
This thesis examines the patterns in one spatial dimension that arise from the study of two predator-prey reaction diffusion systems that includes nonlocal terms. The first model considered was one proposed in Gourley & Britton (1996). However, this model was shown to have serious flaws and consequently a second, improved model was proposed. It is this second model that is the main focus of this thesis. A spatially uniform solution with constant, nonzero numbers of predator and prey exists. A linear stability study of this solution shows that both Hopf and Turing bifurcations can occur along with several types of codimension two bifurcation points. Weakly nonlinear analysis of the Hopf and Turing bifurcations are performed and the results compared with computations. An investigation of the of the codimension two points is also made: one is a Takens-Bogdanov point where both Hopf and steadystate bifurcations meet and the second where Hopf and steady-state bifurcations onset with wavenumber in the ratio 1:2.
Supervisor: Not available Sponsor: Not available
Qualification Name: Not available Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.505166  DOI: Not available
Share: