Coupled quintessence and the impossibility of an interaction: a
  dynamical analysis study
  We analyze the coupled quintessence in the light of the linear dynamical
systems theory, with two different interactions: i) proportional to the energy
density of the dark energy and ii) proportional to the sum of the energy
densities of the dark matter and dark energy. The results presented here
enlarge the previous analyses in the literature, wherein the interaction has
been only proportional to the energy density of the dark matter. In the first
case it is possible to get the well-known sequence of cosmological eras. For
the second interaction only the radiation and the dark energy era can be
described by the fixed points. Therefore, from the point-of-view of the
dynamical system theory, the interaction proportional to the sum of the energy
densities of the dark matter and dark energy does not describe the universe we
live in.
