Cosmological dynamics with non-linear interactions
  We consider a set of non-linear interactions between dark matter and dark
energy which comprises couplings proportional to products of (powers of) the
energy densities of both dark components and of the total energy. We
demonstrate that under such conditions the final state of the Universe may
differ substantially from that of the standard LCDM model. In particular, the
ratio of the energy densities of dark matter and dark energy may approach a
stable finite value or oscillate about such a value. Stationary solutions of
this type require a phantom-type "bare" equation of state of the dark energy
which, however, does not lead to a big-rip singularity. A corresponding
analytic solution for a particular case is shown to be consistent with the
supernova type Ia (SNIa) data from the Union2 set. For a broader class of
interactions, a dynamical system analysis classifies stationary points with
emphasis on their potential relevance for the coincidence problem.
