  In this work we investigate the background dynamics when dark energy is
coupled to dark matter with a suitable interaction in the universe described by
brane cosmology. Here DGP and the RSII brane models have been considered
separately. Dark energy in the form of modified Chaplygin gas is considered. A
suitable interaction between dark energy and dark matter is considered in order
to at least alleviate (if not solve) the cosmic coincidence problem. The
dynamical system of equations is solved numerically and a stable scaling
solution is obtained. A significant attempt towards the solution of the cosmic
coincidence problem is taken. The statefinder parameters are also calculated to
classify the dark energy models. Graphs and phase diagrams are drawn to study
the variations of these parameters. It is also seen that the background
dynamics of modified Chaplygin gas is completely consistent with the notion of
an accelerated expansion in the late universe. Finally, it has been shown that
the universe in both the models follows the power law form of expansion around
the critical point, which is consistent with the known results.
