The counterflow configuration is widely used to study experimentally premixed and non-premixed flame ignition, with the advantage being that the data can be modeled using quasi one-dimensional codes. In this study, experiments and direct numerical simulations were carried out in order to assess the validity of the assumptions of the one-dimensional formulation. Experimentally, particle image velocimetry, shadowgraph, and a high-speed camera were employed to characterize the flow field before ignition, and to capture the ignition position and further evolution of the flame. The modeling involved axisymmetric numerical simulations using detailed molecular transport and chemical kinetic models. Both experiments and simulations revealed that if solid surfaces are present in the vicinity of the jets exit, the flow separates generating recirculation zones that are unstable and result in the bifurcation of the flow field. As a result, for a given set of boundary conditions at the burners' exits, there exists two possible stable states of the flow field which have different velocity and scalars distribution, and the fuel concentration at which ignition occurs was determined to differ for these two states. A novel approach is proposed to correct for the unavoidable radial non-uniformity of the temperature profile at the exit of the heated jet and the conditions that do not result in bifurcation are outlined, so that the results from one-dimensional codes can be compared to the data with confidence.