Phase space analysis and singularity classification for linearly interacting dark energy models

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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).