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IMA Journal of Applied Mathematics Advance Access originally published online on April 16, 2009
IMA Journal of Applied Mathematics 2009 74(4):622-643; doi:10.1093/imamat/hxp009
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© The Author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Travelling waves in the Oregonator model for the BZ reaction

J. H. Merkin{dagger}

Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK

{dagger} Email: amtjhm{at}maths.leeds.ac.uk

Received on July 11, 2008; Revision received July 11, 2008. Accepted on January 18, 2009

Solutions to the travelling wave equations that arise in the two-variable version of the Oregonator model for the Belousov–Zhabotinsky reaction are obtained for small values of the kinetic parameter {epsilon} using the method of matched asymptotic expansions (MAEs). Single-pulse solutions are considered for both oxidation and reduction waves with the MAE approach clearly bringing out the structure of both types of wave. Various regions are derived where the concentrations of the active species HBrO2 and Mox, as well as the concentration of Br– varying quasi-statically with HBrO2 and Mox, undergo significant changes. The lateral extent of these regions is also estimated in terms of the parameter {epsilon}.

Keywords: Belousov-Zhabotinsky reaction; Oregonator model; reaction pulses; travelling waves; matched asymptotic expansions.


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