  We investigate the quintessence scalar field model modified by the
Generalized Uncertainty Principle in the background of a spatially flat
homogeneous and isotropic universe. By performing a dynamical system analysis
we examine the nature of the critical points and their stability for two
potentials, one is the exponential potential and the other is a general
potential. In the case of an exponential potential, we find some new critical
points for this modified quintessence scenario that describe the de Sitter
universe, and these critical points do not appear in the standard quintessence
model with an exponential potential. This is one of the main results of this
work. Now for the general potential our analysis shows that the physical
properties of the critical points remain exactly the same as for the
exponential potential which means that within this modified quintessence
scenario all kind of potentials have same behaviour. This kind of result is
completely new in cosmology because with the change of the potential,
differences are usually expected in all respect.
