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.
