Dynamics of interacting quintessence

In this paper, we investigate coupled quintessence with scaling potential assuming specific forms of the coupling as A namely, αρ˙m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha {\dot{\rho }}_m$$\end{document}, βρ˙ϕ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta {\dot{\rho }}_{\phi }$$\end{document} and σ(ρ˙m+ρ˙ϕ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma ({\dot{\rho }}_m+{\dot{\rho }}_{\phi })$$\end{document}, and present phase space analysis for three different interacting models. We focus on the attractor solutions that can give rise to late time acceleration with ΩDE/ΩDM\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega _{\mathrm{{DE}}}/\Omega _{\mathrm{{DM}}}$$\end{document} of order unity in order to alleviate the coincidence problem.