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Travelling Waves in Near-Degenerate Bistable CompetitionModels

Published online by Cambridge University Press:  27 July 2010

E.O. Alzahrani ,
F.A. Davidson  and
N. Dodds
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Abstract

We study a class of bistable reaction-diffusion systems used to model two competingspecies. Systems in this class possess two uniform stable steady states representingsemi-trivial solutions. Principally, we are interested in the case where the ratio of thediffusion coefficients is small, i.e. in thenear-degenerate case. First, limiting arguments are presented to relatesolutions to such systems to those of the degenerate case where one species is assumed notto diffuse. We then consider travelling wave solutions that connect the two stablesemi-trivial states of the non-degenerate system. Next, a general energy function for thefull system is introduced. Using this and the limiting arguments, we are able to determinethe wave direction for small diffusion coefficient ratios. The results obtained onlyrequire knowledge of the system kinetics.

Keywords

competitionreaction-diffusionfree energybistabletravelling waves
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 5 , Issue 5: Reaction-diffusion waves , 2010 , pp. 13 - 35
Copyright
© EDP Sciences, 2010

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