  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
Einstein-Aether gravity. 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 in Einstein-Aether gravity is
completely consistent with the notion of an accelerated expansion in the late
universe. Finally, it has been shown that the universe follows the power law
form of expansion around the critical point.
