  We consider the field equations for a flat FRW cosmological model, in a
generic $f(R)$ gravity model and cast them into a, completely
normalized-dimensionless, system of O.D.Es for the scale factor and the
function $f(R)$, with respect to the scalar curvature $R$. It is shown that
under reasonable assumptions one can produce simple analytical and numerical
solutions describing bouncing cosmological models where in addition there are
late-time accelerating. Possibility of extending these results is briefly
discussed.
