  The dynamics of matter waves in the atomic to molecular condensate transition
with a time-modulated atomic scattering length is investigated. Both the cases
of rapid and slow modulations are studied. In the case of rapid modulations,
the average over oscillations for the system is derived. The corresponding
conditions for dynamical suppression of the association of atoms into the
molecular field, or of second-harmonic generation in nonlinear optical systems,
are obtained. For the case of slow modulations, we find resonant enhancement in
the molecular field. We then illustrate chaos in the atomic-molecular BEC
system. We suggest a sequential application of the two types of modulations,
slow and rapid, when producing molecules.
