  We explore a cosmological model composed by a dark matter fluid interacting
with a dark energy fluid. The interaction term has the non-linear
lambda*(rho_m)^alpha * (rho_e)^beta form, where rho_m and rho_e are the energy
densities of the dark matter and dark energy, respectively. The parameters
alpha and beta are in principle not constrained to take any particular values,
and were estimated from observations. We perform an analytical study of the
evolution equations, finding the fixed points and their stability properties in
order to characterize suitable physical regions in the phase space of the dark
matter and dark energy densities. The constants (lambda, alpha, beta) as well
as w_m and w_e of the EoS of dark matter and dark energy respectively, were
estimated using the cosmological observations of the type Ia supernovae and the
Hubble expansion rate H(z) data sets. We find that the best estimated values
for the free parameters of the model correspond to a warm dark matter
interacting with a phantom dark energy component, with a well goodness-of-fit
to data. However, using the Bayesian Information Criterion (BIC) we find that
this model is overcame by a warm dark matter -- phantom dark energy model
without interaction, as well as by the LCDM model. We find also a large
dispersion on the best estimated values of the (lambda, alpha, beta)
parameters, so even if we are not able to set strong constraints on their
values, given the goodness-of-fit to data of the model, we find that a large
variety of theirs values are well compatible with the observational data used.
