Unsteady fronts in an auto catalytic system

N. J. Balmforth*, R. V. Craster, S. J. A. Malham

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)


Travelling waves in a model for autocatalytic reactions have, for some parameter regimes, been suggested to have oscillatory instabilities. These instabilities are confirmed by various methods, including linear-stability analysis (exploiting Evans's function) and direct numerical simulations. The front instability sets in when the order of the reaction, m, exceeds some threshold, mc(τ), that depends on the inverse of the Lewis number, τ. The stability boundary, m = mc(τ), is found numerically for m order one. In the limit m ≫ 1 (in which the system becomes similar to combustion systems with Arrhenius kinetics), the method of matched asymptotic expansions is employed to find the asymptotic front speed and show that mc ∼ (V -1)-1 as τ rarr;1. Just beyond the stability boundary, the unstable rocking of the front saturates supercritically. If the order is increased still further, period-doubling bifurcations occur, and for small τ there is a transition to chaos through intermittency after the disappearance of a period-4 orbit.

Original languageEnglish
Pages (from-to)1401-1433
Number of pages33
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number1984
Publication statusPublished - 8 Apr 1999


  • Combustion
  • Instability
  • Travelling waves

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)


Dive into the research topics of 'Unsteady fronts in an auto catalytic system'. Together they form a unique fingerprint.

Cite this