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. 
Fabrizio F. Bernardi and Ricardo G. Landim
gr-qc astro-ph.CO