  The present work is a second in the series of investigation of the background
dynamics in brane cosmology when dark energy is coupled to dark matter by a
suitable interaction. Here, dark matter is chosen in the form of perfect fluid
with barotropic equation of state while a real scalar field with self
interacting potential is chosen as dark energy. The scalar field potential is
chosen as exponential or hyperbolic in nature and three different choices for
the interaction between the dark species are considered. In the background of
spatially flat, homogeneous and isotropic Friedmann-Robertson-Walker (FRW)
brane model, the evolution equations are reduced to an autonomous system by
suitable transformation of variables and a series of critical points are
obtained for different interactions. By analyzing the critical points, we have
found cosmologically viable model describing an early inflationary scenario to
dark energy dominated era connecting through a matter dominated phase.
