  We demonstrate dynamical control of the superradiant transition of cavity-BEC
system via periodic driving of the pump laser. We show that the dominant
density wave order of the superradiant state can be suppressed, and that the
subdominant competing order of Bose-Einstein condensation emerges in the steady
state. Furthermore, we show that additional, non-equilibrium density wave
orders, which do not exist in equilibrium, can be stabilized dynamically.
Finally, for strong driving, chaotic dynamics emerges.
