  In this paper we shall study the phase space of a coupled dark energy-dark
matter fluids system, in which the dark energy has a generalized logarithmic
corrected equation of state. Particularly, the equation of state for the dark
energy will contain a logarithmic function of the dark energy density $\rho_d$
and will also have quadratic and Chaplygin gas-like terms, expressed in terms
of $\rho_d$. We shall use the dynamical system approach in order to study the
cosmological dynamics, and by appropriately choosing the dynamical system
variables, we shall construct an autonomous dynamical system. The study will be
performed in the context of classical and loop quantum cosmology, and the focus
is on finding stable de Sitter attractors. As we demonstrate, in both the
classical and loop quantum cosmology cases, there exist stable de Sitter
attractors in the phase space, with the loop quantum cosmology case though
having a wider range of the free parameter values for which the stable de
Sitter attractors may occur. It is emphasized that the use of a generalized
dark energy equation of state makes possible the existence of de Sitter
attractors, which were absent in the case that a simple logarithmic term
constitutes the dark energy equation of state.
