  Large clouds of cold atoms prepared in a magneto-optical trap are known to
present spatiotemporal instabilities when the frequency of the trapping lasers
is brought close to the atomic resonance. This system bears similarities with
trapped plasmas where the role of the Coulomb interaction is played by the
exchange of scattered photons, and astrophysical objects such as stars whose
size is dependent on radiative forces. We present in this paper a study of the
phase-space of such instabilities, and reveal different dynamical regimes.
Three dimensional simulations of the highly nonlinear atomic dynamics permit a
detailed analysis of the experimental observations.
