  The simplest model of three coupled Bose-Einstein Condensates (BEC) is
investigated using a group theoretical method. The stationary solutions are
determined using the SU(3) group under the mean field approximation. This
semiclassical analysis using the system symmetries shows a transition in the
dynamics of the system from self trapping to delocalization at a critical value
for the coupling between the condensates. The global dynamics are investigated
by examination of the stable points and our analysis shows the structure of the
stable points depends on the ratio of the condensate coupling to the
particle-particle interaction, undergoes bifurcations as this ratio is varied.
This semiclassical model is compared to a full quantum treatment, which also
displays the dynamical transition. The quantum case has collapse and revival
sequences superposed on the semiclassical dynamics reflecting the underlying
discreteness of the spectrum. Non-zero circular current states are also
demonstrated as one of the higher dimensional effects displayed in this system.
