  Motivated by the experimental realization of Dicke model in optical cavities,
we model an optomechanical system consisting of a two level BEC with transverse
pumping. We investigate the transition from normal and inverted state to the
superradiant phase through a detailed study of the phase portrait of the
system. The rich phase portrait generated by analytic arguments displays two
types of superradiant phases, regions of coexistence and some portion
determining the persistent oscillations. We study the time evolution of the
system from any phase and discuss the role of mirror frequency in achieving the
attractors and stable values. Further, we add an external mechanical pump to
the mirror which is capable of changing the mirror frequency and study the
impact of the pump on the phase portraits and the dynamics of the system. We
find the external mirror frequency changing the phase portraits and even
shifting the critical transition point, thereby predicting a system with
controllable phase transition.
