  In a trapped Bose-Einstein condensate, subject to the action of an
alternating external field, coherent topological modes can be resonantly
excited. Depending on the amplitude of the external field and detuning
parameter, there are two principally different regimes of motion, with mode
locking and without it. The change of the dynamic regime corresponds to a
dynamic phase transition. This transition can be characterized by an effective
order parameter defined as the difference between fractional mode populations
averaged over the temporal period of oscillations. The behavior of this order
parameter, as a function of detuning, pumping amplitude, and atomic
interactions is carefully analyzed. A special attention is payed to numerical
calculations for the realistic case of a quadrupole exciting field and the
system parameters accessible in current experiments.
