  We investigate a simplified kinetic system of the hydrogen atom (two levels
plus continuum) under conditions of a type IIP supernova at the plateau phase
that realistically describes the basic properties of the complete system. We
have found the Lyapunov function for the reduced system using which we have
analytically obtained the ionization freeze-out effect on long time scales.
Since the system completely recombines in the equilibrium approximation on long
time scales, which does not occur in reality, this result confirms the
necessity of allowance for the time-dependent effect in the kinetics during the
photospheric phase in a supernova explosion.
