  This work contains a detailed qualitative analysis, in General Relativity and
in Loop Quantum Cosmology, of the dynamics in the associated phase space of a
scalar field minimally coupled with gravity, whose potential mimics the
dynamics of a perfect fluid with a linear Equation of State (EoS). Dealing with
the orbits (solutions) of the system, we will see that there are analytic ones,
which lead to the same dynamics as the perfect fluid, and our goal is to check
their stability, depending on the value of the EoS parameter, i.e., to show
whether the other orbits converge or diverge to these analytic solutions at
early and late times.
