Fronts, relaxation oscillations, and period doubling in solid fuel combustion

A. Bayliss*, B. J. Matkowsky

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

77 Scopus citations


We consider a reaction-diffusion system which models the gasless combustion of a solid material. The system exhibits oscillating fronts, whose nature varies as a function of the parameters of the problem. The behavior of the solution along the bifurcation branches is studied numerically, by an adaptive Chebychev pseudo-spectral method in which the coordinate system is adapted to follow the sharp oscillations of the front. As the bifurcation parameter is increased through a primary bifurcation point, the solution exhibits a transition from a steadily propagating front to a sinusoidally oscillating front. This front develops into a relaxation oscillation whose peaks become progressively sharper and steeper. As a secondary bifurcation point is exceeded, a period-doubling bifurcation occurs.

Original languageEnglish (US)
Pages (from-to)147-168
Number of pages22
JournalJournal of Computational Physics
Issue number1
StatePublished - Jul 1987

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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