  Two distinct strongly non-linear scenarios of molecule formation in an atomic
Bose-Einstein condensate (either by photoassociation or Feshbach resonance)
corresponding to large and small field detuning are revealed. By examining
arbitrary external field configurations, we show that the association process
in the first case is almost non-oscillatory in time while in the second case
the evolution of the system displays strongly pronounced Rabi-type
oscillations. We construct highly accurate approximate solutions for both limit
cases. We show that at strong coupling limit the non-crossing models are able
to provide conversion of no more than one third of the initial atomic
population. Finally, we show that for constant-amplitude models involving a
finite final detuning the strong interaction limit is not optimal for molecule
formation.
