A dynamical systems analysis of interacting dark energy models
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We investigate using dynamical system analysis; the impacts of various interaction models whereby dark energy is coupled with dark matter. Examination on the nature of critical points for each interaction model introduced was conducted in order to obtain the cosmological consequence of each choice of interaction, with all the components of the universe considered, namely, the radiation, matter, and dark energy dominated universes. The existence of unstable radiation epoch, unstable dark matter epoch, and stable dark energy epoch will be shown for models displaying cosmologically acceptable results. Using the value of the scale factor at equality we determine the time at which the matter-dark energy equality occurred for each model. Constraints on the coupling constant b of the interacting dark energy models were placed in order to determine the phantom or quintessence behaviour of the equation of state for dark energy. We do model comparison and also compare with the LCDM, so as to filter our models for the best possible form of interaction term between dark matter and dark energy.