  One possible description for the current accelerated expansion of the
universe is quintessence dynamics. The basic idea of quintessence consists of
analyzing cosmological scenarios driven by scalar fields. In this work we
present some interesting features on the cosmological scenario obtained from
the solutions of an effective two scalar field model in a flat space-time. This
effective model was constructed by coupling two single scalar field systems in
a nontrivial way via an extension method. The solutions related to the fields
allowed us to compute analytical cosmological parameters. The behavior of these
parameters are highlighted, as well as the different epochs obtained from them.
