Pulsating regimes of flames propagation in a model with chain-branching reaction

In this paper we investigate propagation of planar combustion waves in an adiabatic model with two-step chain branching reaction mechanism. Pulsating instabilities are found to emerge for fuel Lewis number greater than one due to a Hopf bifurcation. The Hopf bifurcation is demonstrated to be of a supercritical nature and it gives rise to periodic pulsating combustion waves as the neutral stability boundary is crossed. Further increase of the bifurcation parameter initiates period doubling bifurcation cascade and leads to chaotic regime of combustion wave propagation. The chaotic wave extinguishes when the bifurcation parameter becomes sufficiently large.