  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.
