A one-dimensional model for the so-called pulsed flames, which are emp
loyed for molecular detection and in some combustion related measureme
nts, is formulated and studied numerically. It is shown that the pulse
d flame is in fact a highly nonlinear realization of the classical osc
illatory instability of the anchored flame. Yet to maintain the pulsed
flame within the detector's tube one may need an external heat source
adapting the pulsations amplitude to the tube length.