Qualitative study of anisotropic cosmological models with dark sector coupling

In this paper, we study the dynamical evolution of locally rotationally symmetric (LRS) Bianchi type I cosmological model with coupling of dark sector. We investigate the phase-plane analysis when dark energy is modelled as exponential quintessence, and is coupled to dark energy matter via linear coupling between both dark components. The evolution of cosmological solutions is studied by using dynamical systems techniques. Stability and viability issues for three different physically viable linear couplings between both dark components are presented and discussed in detail. (author)