Modelling of the positive column in the glow discharge of neon was performed under discharge conditions covering the areas of diffuse and constricted states, as well as the transition region between them. An analysis of the stability of the stationary solution for diffuse and constricted regimes of the discharge was made. The spectral problem was solved in order to find the eigenmodes and eigenvalues corresponding to the growth increment of the perturbations of the electron number density and electrical potential. It was shown that the discharge in the diffusion mode is stable with respect to the perturbations under consideration, and the appearance and propagation of essentially two-dimensional spatially periodic perturbations is possible in the constricted mode of the discharge. A two-dimensional structure (topology) of plasma parameters was calculated and illustrated. The results of the theory were compared to the experimental data.