The Mathematical Institute, University of Oxford, Eprints Archive

Long-term coexistence for a competitive system of spatially varying gradient reaction-diffusion equations

Korobeinikov, Andrei and Norbury, John and Wake, Graeme (2007) Long-term coexistence for a competitive system of spatially varying gradient reaction-diffusion equations. Nonlinear Analysis Series B: Real World Applications . ISSN 1468-1218 (Submitted)

[img]
Preview
PDF
175Kb

Abstract

Spatial distribution of interacting chemical or biological species is usually described by a system of reaction-diffusion 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 long-term coexistence of the species in a bounded domain. Such long-term coexistence may be associated either with a periodic in time solution (usually associated with a Hopf bifurcation), or with time-independent solutions. We prove that no periodic solution exists for the system. We also consider some steady-states (the time-independent 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:20 Jul 2009 14:23

Repository Staff Only: item control page