The stability criteria for spatially flat homogeneous and isotropic cosmological dynamical system is investigated with the interaction of a scalar field endowed with a perfect fluid.In this paper, we depict the dynamical system perspective to study, qualitatively, the scalar field cosmology under two special cases, with and without potential. For analysis with potential we use simple exponential potential form, $V_{o}e^{-lambda phi}$. We generate, by introducing new dimensionless variables, an autonomous system of ordinary differential equations $(ASODE)$ for each case and obtain respective fixed points. We also analyse the type of fixed points, nature and stability of the fixed points and how their nature and behavior reflect towards the cosmic scenarios. Throughout the whole work, the investigation of this model has shown us the deep connection between these theories and cosmic acceleration phenomena. The phase plots of the system at different conditions and different values of $gamma$ have been analyzed in detail and their interpretations have been worked out.The perturbation plots of the dynamical system have also been studied and analyzed which emphasize our analytical findings.
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