  In this work we establish only at background dynamics level, the equivalence
between the Created Cold Dark Matter (CCDM) model and diverse dark energy (DE)
models. We find that for a barotropic or linear equation of state (EoS) for the
DE, $p=w \rho$, and standard matter sector the corresponding CCDM model is
described by the same functional structure of the ratio of particle production,
$\Gamma$. For a different EoS the functional form of the $\Gamma$ term is not
longer maintained, however, in the case of a polytropic EoS given by the
Chaplygin gas the resulting $\Gamma$ term can be written as the one obtained in
the barotropic case under certain considerations.
