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

By Andrei Korobeinikov, John Norbury and Graeme Wake

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

Topics: Partial differential equations
Year: 2007
OAI identifier: oai:generic.eprints.org:638/core69

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