The methods of nonlinear dynamics are used to study the equation of balance of charged particles in the plasma of an inert gas discharge when the loss of these particles is due to ambipolar diffusion to the walls and volume recombination. A property of the problem is a strong nonlinear electron-density dependence of the ionization rate as the result of the competition of electron-atom and electron-electron collisions. It is shown that the contraction of the discharge at pressures above a critical pressure can be regarded as a phase transition to a new dissipative structure.