  The stability analysis of a generalized Dicke model, in the semi-classical
limit, describing the interaction of a two-species Bose-Einstein condensate
driven by a quantized field in the presence of Kerr and spontaneous parametric
processes is presented. The transitions from Rabi to Josephson dynamics are
identified depending on the relative value of the involved parameters.
Symmetry-breaking dynamics are shown for both types of coherent oscillations
due to the quantized field and nonlinear optical processes.
