  We propose a cosmological model that makes a significant step toward solving
the coincidence problem of the near similarity at the present of the dark
energy and dark matter components. Our cosmology has the following properties:
a) among flat and homogeneous spaces, the present universe is a global
attractor: all the possible initial conditions lead to the observed proportion
of dark energy and dark matter; once reached, it remains fixed forever; b) the
expansion is accelerated at the present, as requested by the supernovae
observations; c) the model is consistent with the large-scale structure and
microwave background data; d) the dark energy and the dark matter densities
always scale similarly after equivalence and are close to within two orders of
magnitude. The model makes use of a non-linear coupling of the dark energy to
the dark matter that switches on after structure formation.
