  We investigate the dynamics of an open Bose-Einstein condensate system
consisting of two hyperfine states of the same atomic species which are coupled
by tunable Raman laser. It is already suggested that the detuning between the
laser frequency and transition frequency affect significantly on the dynamics
of the pure condensate. Here we show that the detuning effect is suppressed by
noise and dissipation caused by the environment. The increase of coherence and
purity are also displayed for specific parameters. As a verification to the
lowest-order approximation we derive the hierarchy of motion equations in the
second-order approximation. It turns out that the former one can describe the
dynamical evolution qualitatively for weak noise and dissipation and
quantitatively for strong noise and dissipation.
