A bifurcation analysis is made of the transition of steady-state discharges from a diffuse to a contracted state. It is shown that such experimentally observable characteristics of the contraction effect as sudden changes and hysteresis manifest the bifurcations studied here only when the influence of electron-electron collisions on the ionization rate is taken into account. When this influence is ignored, nonuniform heating of the gas creates a soft transcritical bifurcation that is accompanied by smooth changes in the internal parameters of the plasma. The dependence of the ratio of the ionization and recombination rates on the electron density for a given longitudinal field and electron temperature has a decisive effect on the character of the bifurcation. When electron-electron collisions are included, this function has a minimum for densities of ≈ 10¹¹ cm^-3. The nonmonotonicity of this function creates a Z-shaped region in the bifurcation diagram that corresponds to two hard bifurcations of the saddle-node type and the appearance of hysteresis.