The evolution of travelling waves from chemical-clock reactions

S. J. Preece, J. Billingham and A. C. King
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S. J. Preece: University of Birmingham, School of Mathematics and Statistics
J. Billingham: University of Birmingham, School of Mathematics and Statistics
A. C. King: University of Birmingham, School of Mathematics and Statistics

A chapter in Practical Asymptotics, 2001, pp 367-385 from Springer

Abstract: Abstract A clock-reaction is a chemical reaction which gives rise to an initial induction period before a significant change in concentration of one of the chemical species occurs. In this paper the development of travelling waves from a particular class of inhibited autocatalytic clock-reactions is analysed. The numerical solutions show that, after the induction period, a propagating reaction-diffusion front is initiated. This front is seen to accelerate initially and then to become a constant-speed travelling wave. An asymptotic analysis of the large-time travelling-wave behaviour is given and from this it is possible to fix a minimum wave speed. The asymptotic predictions of the wave speed are found to agree well with those of the numerical solution.

Keywords: clock-reaction; autocatalysis; inhibition; reaction-diffusion; travelling wave (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-010-0698-9_16

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DOI: 10.1007/978-94-010-0698-9_16

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