  We discuss the dynamics of classical Dicke-type models, aiming to clarify the
mechanisms by which coherent states could develop in potentially
non-equilibrium systems such as semiconductor microcavities. We present
simulations of an undamped model which show spontaneous coherent states with
persistent oscillations in the magnitude of the order parameter. These states
are generalisations of superradiant ringing to the case of inhomogeneous
broadening. They correspond to the persistent gap oscillations proposed in
fermionic atomic condensates, and arise from a variety of initial conditions.
We show that introducing randomness into the couplings can suppress the
oscillations, leading to a limiting dynamics with a time-independent order
parameter. This demonstrates that non-equilibrium generalisations of polariton
condensates can be created even without dissipation. We explain the dynamical
origins of the coherence in terms of instabilities of the normal state, and
consider how it can additionally develop through scattering and dissipation.
