  The dynamics of Bose-Einstein condensates in asymmetric double-wells is
studied. We construct a two-mode model and analyze the properties of the
corresponding phase-space diagram, showing in particular that the minimum of
the phase-space portrait becomes shifted from the origin as a consequence of
the nonvanishing overlap between the ground and excited states from which the
localized states are derived. We further incorporate effective interaction
corrections in the set of two-mode model parameters. Such a formalism is
applied to a recent experimentally explored system, which is confined by a
toroidal trap with radial barriers forming an arbitrary angle between them. We
confront the model results with Gross-Pitaevskii simulations for various angle
values finding a very good agreement. We also analyze the accuracy of a
previously employed simple model for moving barriers, exploring a possible
improvement that could cover a wider range of trap asymmetries.
