  In this paper we investigate dynamics of the modified loop quantum cosmology
models using dynamical systems methods. Modifications considered come from the
choice of the different field strength operator $\hat{F}$ and result in
different forms of the effective Hamiltonian. Such an ambiguity of the choice
of this expression from some class of functions is allowed in the framework of
loop quantisation. Our main goal is to show how such modifications can
influence the bouncing universe scenario in the loop quantum cosmology. In
effective models considered we classify all evolutional paths for all
admissible initial conditions. The dynamics is reduced to the form of a
dynamical system of the Newtonian type on a 2-dimensional phase plane. These
models are equivalent dynamically to the FRW models with the decaying effective
cosmological term parametrised by the canonical variable $p$ (or by the scale
factor $a$). We find that for the positive cosmological constant there is a
class of oscillating models without the initial and final singularities. The
new phenomenon is the appearance of curvature singularities for the finite
values of the scale factor, but we find that for the positive cosmological
constant these singularities can be avoided. For the positive cosmological
constant the evolution begins at the asymptotic state in the past represented
by the deSitter contracting (deS$_{-}$) spacetime or the static Einstein
universe H=0 or $H=-\infty$ state and reaches the deSitter expanding state
(deS$_{+}$), the state H=0 or $H=+\infty$ state. In the case of the negative
cosmological constant we obtain the past and future asymptotic states as the
Einstein static universes.
