  The cloud of cold atoms obtained from a magneto-optical trap is known to
exhibit two types of instabilities in the regime of high atomic densities:
stochastic instabilities and deterministic instabilities. In the present paper,
the experimentally observed stochastic dynamics is described extensively. It is
shown that it exists a variety of dynamical behaviors, which differ by the
frequency components appearing in the dynamics. Indeed, some instabilities
exhibit only low frequency components, while in other cases, a second time
scale, corresponding to a higher frequency, appears in the motion of the center
of mass of the cloud. A one-dimensional stochastic model taking into account
the shadow effect is shown to be able to reproduce the experimental behavior,
linking the existence of instabilities to folded stationary solutions where
noise response is enhanced. The different types of regimes are explained by the
existence of a relaxation frequency, which in some conditions is excited by
noise.
