Bistability of flame propagation in a model with competing exothermic reactions

Abstract

We investigate a diffusional-thermal model with two-step competitive exothermic reactions for premixed combustion wave propagation in one spatial dimension under adiabatic conditions. A criterion based on the crossover temperature notion was used to qualitatively predict the region in the space of parameters where three travelling combustion wave solutions coexist, which are further studied via numerical means. It is demonstrated that under certain conditions the flame speed is an ‘S’-shaped function of parameters. The fast branch is either stable or is partly stable and exhibits the Andronov–Hopf (AH) bifurcation before the turning point is reached. The mid-branch is completely unstable. The slow solution branch is either unstable or partly stable and exhibits a single or a pair of AH bifurcations. The AH bifurcations are shown to be supercritical giving rise to stable pulsating waves. Bistability and hysteresis phenomena are also demonstrated.