  A chirped parametrically driven discrete nonlinear Schrodinger equation is
discussed. It is shown that the system allows two resonant excitation
mechanisms, i.e., successive two-level transitions (ladder climbing) or a
continuous classical-like nonlinear phase-locking (autoresonance). Two-level
arguments are used to study the ladder-climbing process, and semiclassical
theory describes the autoresonance effect. The regimes of efficient excitation
in the problem are identified and characterized in terms of three dimensionless
parameters describing the driving strength, the dispersion nonlinearity, and
the Kerr-type nonlinearity, respectively. The nonlinearity alters the
borderlines between the regimes, and their characteristics.
