[en] The influence of small radial perturbations of the cathode current on the characteristics of a homogeneous barrier discharge in nitrogen is investigated on the basis of a two-dimensional fluid model. In a Townsend discharge, radial fluctuations are substantially suppressed, which is the evidence of its stability. The oscillative mode of the Townsend discharge is also stable with regard to radial perturbations. As the discharge turns into a form controlled by spatial charge (a streamer is developed), disturbances of all radii grow in time. Such a behaviour testifies the instability of a streamer front and may cause the discharge filamentation. Since only the Townsend discharge is stable, it is possible to use a one-dimensional model to determine the domain of existence for a homogeneous discharge. The study of homogeneity domains by means of the one-dimensional model shows that at relatively large values of the voltage growth rate, discharge gap width, or capacitance of dielectric barriers the discharge tends to be filamentary. Calculation of the domain of the discharge homogeneity agrees satisfactory with the experimental data available as the account is taken for the gas heating