Interacting dark energy: Dynamical system analysis

We investigate the impacts of interaction between dark matter (DM) and dark energy (DE) in the context of two DE models, holographic (HDE) and ghost dark energy (GDE). 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 DE. Studying the phase space for all interactions in detail, we show the existence of unstable matter-dominated and stable DE-dominated phases. We also show that linear interactions suffer from the absence of standard radiation-dominated epoch. Interestingly, this failure resolved by adding the nonlinear interactions to the models. We find an upper bound for the value of the coupling constant of the interaction between DM and DE as b < 0.57 in the case of holographic model, and b < 0.61 in the case of GDE 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.