  The non-equilibrium statistics and kinetics of a simple bistable system
(resonantly driven nonlinear oscillator coupled to reservoir) have been
investigated by means of master equation for the density matrix and
quasiclassical Fokker-Planck equation in quasienergy space. We found out that
the system's statistical and kinetic properties drastically change when the
quasienergy states become nearly degenerate and the occupation of the most
excited state is strongly enhanced. It has been revealed that in nearly
degenerate case a new critical quasienergy parameter emerges. Below the
critical quasienergy value the eigenstates are superpositions of the
quasiclassical states from different phase space regions, while above this
value the eigenstates correspond to only one particular region of the phase
space. We have also generalized Keldysh theory for ionization of atoms in the
electromagnetic field for bistable systems. It has been demonstrated that
Keldysh parameter in bistability region is large when pumping intensity is
smaller than the critical value. It has been shown by direct calculations that
multi-photon transition amplitude coincides with the tunneling amplitude. So,
multi-photon transitions and tunneling between the regions of the phase space
are just the same effects. We also demonstrated that for bistable systems the
Keldysh parameter logarithmically depends on the external field amplitude.
