Title: Dynamical system analysis of dark energy models in scalar coupled metric-torsion theories,
Abstract: We study the phase space dynamics of cosmological models in the theoretical
formulations of non-minimal metric-torsion couplings with a scalar field, and
investigate in particular the critical points which yield stable solutions
exhibiting cosmic acceleration driven by the {\em dark energy}. The latter is
defined in a way that it effectively has no direct interaction with the
cosmological fluid, although in an equivalent scalar-tensor cosmological setup
the scalar field interacts with the fluid (which we consider to be the
pressureless dust). Determining the conditions for the existence of the stable
critical points we check their physical viability, in both Einstein and Jordan
frames. We also verify that in either of these frames, the evolution of the
universe at the corresponding stable points matches with that given by the
respective exact solutions we have found in an earlier work (arXiv: 1611.00654
[gr-qc]). We not only examine the regions of physical relevance for the
trajectories in the phase space when the coupling parameter is varied, but also
demonstrate the evolution profiles of the cosmological parameters of interest
along fiducial trajectories in the effectively non-interacting scenarios, in
both Einstein and Jordan frames.