  In the proposed model with interaction between dark energy and dark matter,
we consider cosmological scenarios with different equations of state ($w_d$)
for dark energy. For both constant and variable equation of state, we analyze
solutions for dark energy and dark matter in seven variants of the model. We
investigate exact analytic solutions for $w_d={}$ constant equation of state,
and several variants of the model for variable $w_d$. These scenarios are
tested with the current astronomical data from Type Ia Supernovae, baryon
acoustic oscillations, Hubble parameter $H (z)$ and the cosmic microwave
background radiation. Finally, we make a statistical comparison of our
interacting model with $\Lambda$CDM as well as with some other well known
non-interacting cosmological models.
