  The dynamics of stability and collapse of a trapped atomic Bose-Einstein
condensate (BEC) coupled to a molecular one is studied using the time-dependent
Gross-Pitaevskii (GP) equation including a nonlinear interaction term which can
transform two atoms into a molecule and vice versa. We find interesting
oscillation of the number of atoms and molecules for a BEC of fixed mass. This
oscillation is a consequence of continuous transformation in the condensate of
two atoms into a molecule and vice versa. For the study of collapse an
absorptive contact interaction and an imaginary quartic three-body
recombination term are included in the GP equation. It is possible to have a
collapse of one or both components when one or more of the nonlinear terms in
the GP equation are attractive in nature, respectively.
