Dynamical system analysis of quintom dark energy model

The present work deals with dynamical system analysis of a quintom model of dark energy. By suitable transformation of variables the Einstein field equations are converted to an autonomous system. The critical points are determined and stability of hyperbolic critical points are determined by Hartman-Grobman theorem. To analyze non-hyperbolic critical points different tools (notably center manifold theory) are used. Possible bifurcation scenarios have also been explained.