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

Classical dynamics of a two-species Bose-Einstein condensate in the presence of nonlinear maser processes