  We consider a spatially flat FLRW universe. We assume that it is filled with
dark energy in the form of logotropic dark fluid coupled with dark matter in
the form of a perfect fluid having a barotropic equation of state. We employ
dynamical system tools to obtain a complete qualitative idea of the evolution
of such a universe. It is interesting to note that we ought to consider an
approximation for the pressure of the logotropic dark fluid in the form of an
infinite series so as to be able to construct the autonomous system required
for a dynamical system study. This series form provides us with a power law in
the rest-mass energy density of the logotropic dark fluid. We compute the
critical points of the autonomous system and analyze these critical points by
applying linear stability theory. Our analysis reveal a scenario of late-time
accelerated universe dominated by the logotropic fluid which behaves as
cosmological constant, preceded by an intermediate phase of the Universe
dominated by logotropic fluid which behaves as dark matter in the form of
perfect fluid. Moreover, it also crosses the phantom divide line.
