  The dynamics of a mean-field model of three coupled condensates is studied
for initial states characterized by twin condensates. Condensates occupy an
open three-well chain, where the central potential-well depth is an independent
parameter. Despite its diversity from the closed-chain symmetric model, such
model is shown to have an integrable regime involving a predictable evolution
for twin-condensate initial states. After establishing the dependence of the
phase-space topology on the model parameters, the latter are shown to allow the
control of various macroscopic effects such as rapid population inversions,
pulsed phase changes, self-trapping and long-duration periodic oscillations.
Finally, based on quantizing the system in terms of suitable ``microscopic''
canonical variables, the stability conditions of the integrable regime are
related to the su(1,1) structure of the Hamiltonian spectrum.
