  The present work deals with the dynamical system investigation of interacting
dark energy models (quintessence and phantom) in the framework of Loop Quantum
Cosmology by taking into account a broad class of self-interacting scalar field
potentials. The main reason for studying potentials beyond the exponential type
is to obtain additional critical points which can yield more interesting
cosmological solutions. The stability of critical points and the asymptotic
behavior of the phase space are analyzed using dynamical system tools and
numerical techniques. We study two class of interacting dark energy models and
consider two specific potentials as examples: the hyperbolic potential and the
inverse power-law potential. We found a rich and interesting phenomenology
including the avoidance of big rip singularities due to loop quantum effects,
smooth and non-linear transitions from matter domination to dark energy
domination and finite periods of phantom domination with dynamical crossing of
the phantom barrier.
