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.

22 pages, 7 figures, 2 tables. Replacement with the published version