  The population dynamics of a trapped Bose-Einstein condensate, subject to the
action of an oscillatory field, is studied. This field produces a modulation of
the trapping potential with the frequency close to the transition frequency
between the ground state and an excited energy level. Unusual critical effects
are found exhibiting sharp qualitative changes in the population dynamics. An
effective averaged system is constructed explicitly illustrating the occurrence
of critical phenomena. The related critical indices are calculated.
