A Dynamical System Analysis of Three Fluid cosmological Model

Abstract: In Friedman-Robertson-Walker flat spacetime, we consider a three fluid cosmological model which contains dark matter, dark energy and baryonic matter in the form of perfect fluid with a barotropic equation of state. Dark matter is taken in form of dust and dark energy is described by a scalar field with a potential $V(\phi)$. Einstein's field equations are reduced to an autonomous dynamical system by suitable redefinition of basic variables. Considering exponential potential for the scalar field, critical points are obtained for the autonomous system. Finally stability of the critical points and cosmological implications are analyzed.