  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 deterministic dynamics is described extensively.
Three different behaviors are distinguished. All are cyclic, but not
necessarily periodic. Indeed, some instabilities exhibit a cyclic behavior with
an erratic return time. A one-dimensional stochastic model taking into account
the shadow effect is shown to be able to reproduce the experimental behavior,
linking the instabilities to a several bifurcations. Erraticity of some of the
regimes is shown to be induced by noise.
