Korobeinikov, Andrei and Norbury, John and Wake, Graeme (2007) Longterm coexistence for a competitive system of spatially varying gradient reactiondiffusion equations. Nonlinear Analysis Series B: Real World Applications . ISSN 14681218 (Submitted)

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Abstract
Spatial distribution of interacting chemical or biological species is usually described by a system of reactiondiffusion equations. In this work we consider a system of two reaction diffusion equations with spatially varying diffusion coefficients which are different for different species and with forcing terms which are the gradient of a spatially varying potential. Such a system describes two competing biological species. We are interested in the possibility of longterm coexistence of the species in a bounded domain. Such longterm coexistence may be associated either with a periodic in time solution (usually associated with a Hopf bifurcation), or with timeindependent solutions. We prove that no periodic solution exists for the system. We also consider some steadystates (the timeindependent solutions) and examine their
stability and bifurcations.
Item Type:  Article 

Subjects:  O  Z > Partial differential equations 
Research Groups:  Oxford Centre for Industrial and Applied Mathematics 
ID Code:  638 
Deposited By:  Richard Booth 
Deposited On:  22 Aug 2007 
Last Modified:  29 May 2015 18:25 
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