  We present the results of a series of N-body simulations in cosmologies where
dark matter (DM) is coupled to dark energy (DE), so easing the cosmic
coincidence problem. The dark-dark coupling introduces two novel effects in
N-body dynamics: (i) DM particle masses vary with time; (ii) gravity between DM
particles is ruled by a constant $G^{*}$, greater than Newton's constant $G$,
holding in other 2-body interactions. As a consequence, baryons and DM particle
distributions develop a large scale bias. Here we investigate DE models with
Ratra-Peebles (RP) potentials; the dark-dark coupling is set in a parametric
range compatible with observations, for as concern background and linear
perturbation properties. We study the halo mass function, the halo density
profile and the behavior of the non-linear bias. We find that non-linear
dynamics puts additional constraints to the coupling parameter. They mostly
arise from density profiles, that we find to yield higher concentrations, in
coupled RP models, with respect to (uncoupled) dynamical DE cosmologies. Such
enhancement, although being a strong effect in some coupling parameter range,
is just a minor change for smaller but significant values of the coupling
parameter. With these further restrictions, coupled DE models with RP potential
are consistent with non-linear observables.
