  We investigate the impacts of interaction between dark matter and dark energy
in the context of two dark energy models, holographic and ghost dark energy. In
fact, using the dynamical system analysis, we obtain the cosmological
consequence of several interactions, considering all relevant component of
universe, i.e. matter (Dark and luminous), radiation and dark energy. Studying
the phase space for all interactions in detail, we show the existence of
unstable matter dominated and stable dark energy dominated phases. We also show
that linear interactions suffer from the absence of standard radiation
dominated epoch. Interestingly, this failure resolved by adding the non-linear
interactions to the models. We find an upper bound for the value of the
coupling constant of the interaction between dark matter and dark energy as b <
0.57 in the case of holographic model, and b < 0.61 in the case of ghost dark
energy model, to result in a cosmological viable matter dominated epoch. More
specifically, this bound is vital to satisfy instability and deceleration of
matter dominated epoch.
