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We extend the investigation of cosmological dynamics of the generalnon-canonical scalar field models by dynamical system techniques for a broadclass of potentials and coupling functions. In other words, we do not restrictthe analysis to exponential or power-law potentials and coupling functions.This type of investigation helps in understanding the general properties of aclass of cosmological models. In order to better understand the phase space ofthe models, we investigate the various special cases and discuss the stabilityand viability issues. Performing a detailed stability analysis, we show that itis possible to describe the cosmic history of the universe at the backgroundlevel namely the early radiation dominated era, intermediate matter dominatedera and the late time dark energy domination. Moreover, we find that we canidentify a broad class of coupling functions for which it is possible to get anappealing unified description of dark matter and dark energy. The resultsobtained here, therefore, enlarge the previous analyses wherein only a specificpotential and coupling functions describes the unification of dark sectors.Further, we also observe that a specific scenario can also possibly explain thephenomenon of slow-roll inflationary exit.

Cosmological dynamics of the general non-canonical scalar field models