  In this paper, applying the Hartman-Grobman theorem we carry out a
qualitative late-time analysis of some unified dark energy-matter Friedmann
cosmological models, where the two interact through linear energy exchanges,
and the dark energy fluid obeys to the dynamical equation of state of
Redlich-Kwong, Modified Berthelot, and Dieterici respectively. The
identification of appropriate late-time attractors allows to restrict the range
of validity of the free parameters of the models under investigation. In
particular, we prove that the late-time attractors which support a negative
deceleration parameter correspond to a de Sitter universe. We show that the
strength of deviation from an ideal fluid for the dark energy does not
influence the stability of the late-time attractors, as well as the values of
all the cosmological parameters at equilibrium, but for the Hubble function
(which represents the age of the universe). Our analysis also shows that a
singularity in the effective equation of state parameter for the dark energy
fluid is not possible within this class of models.
