  In this work we consider Randall-Sundrum brane-world type scenarios, in which
the spacetime is described by a five-dimensional manifold with matter fields
confined in a domain wall or three-brane. We present the results of a
systematic analysis, using dynamical systems techniques, of the qualitative
behaviour of the Friedmann-Lemaitre-Robertson-Walker and the Bianchi I and V
cosmological models in these scenarios. We construct the state spaces for these
models and discuss how their structure changes with respect to the
general-relativistic case, in particular, what new critical points appear and
their nature, the occurrence of bifurcations and the dynamics of anisotropy.
