  A general analysis of the induced brane dynamics is performed when the
intrinsic curvature term is included in the action. Such a term is known to
cause dramatic changes and is generically induced by quantum corrections coming
from the bulk gravity and its coupling with matter living on the brane. The
induced brane dynamics is shown to be the usual Einstein dynamics coupled to a
well defined modified energy-momentum tensor. In cosmology, conventional
general relativity revives for an initial era whose duration depends on the
value of the five-dimensional Planck mass. Violations of energy conditions may
be possible, as well as matter inhomogeneities on the brane in (A)dS_{5} or
Minkowski backgrounds. A new anisotropic cosmological solution is given in the
above context. This solution, for a fine-tuned five-dimensional cosmological
constant, exhibits an intermediate accelerating phase which is followed by an
era corresponding to a 4D perfect fluid solution with no future horizons.
