  Motivated by experiments observing self-organization of cold atoms in optical
cavities we investigate the collective dynamics of the associated
nonequilibrium Dicke model. The model displays a rich semiclassical phase
diagram of long time attractors including distinct superradiant fixed points,
bistable and multistable coexistence phases and regimes of persistent
oscillations. We explore the intrinsic timescales for reaching these asymptotic
states and discuss the implications for finite duration experiments. On the
basis of a semiclassical analysis of the effective Dicke model we find that
sweep measurements over 200ms may be required in order to access the asymptotic
regime. We briefly comment on the corrections that may arise due to quantum
fluctuations and states outside of the effective two-level Dicke model
description.
