A laterally extended dc-driven system of planar gas discharge with a high-ohmic semiconductor electrode is considered. Numerical models are based on the fluid equations of plasma with drift-diffusion approximation for particle fluxes. The effect of different modelling approaches (with simpler and more detailed treatment of the electron transport and plasma chemical reactions) is analyzed. Bifurcation diagrams separating stable stationary states of the system from oscillatory states are derived and compared with the experimental data. Published by AIP Publishing.