  In this paper, we consider spatially flat FLRW cosmological models in two
contexts in an attempt to derive a set of conditions that characterize when
such models exhibit oscillatory behaviour. In the first case, we consider a
spatially flat FLRW model with only a minimally-coupled scalar field, described
by a nonnegative scalar field potential. In the second case, we extended this
model to include barotropic matter. We show that for the case of a positive
cosmological constant, spatial flatness, and barotropic matter, oscillatory
solutions are certainly possible. However, these solutions do not oscillate
indefinitely, they decay over time. Interestingly, it is shown that all such
solutions oscillate and decay towards the de Sitter equilibrium point, which
represents an inflationary epoch in such models. This implies that for certain
families of scalar field potentials, the universe may have undergone several
oscillations \emph{before} entering an inflationary epoch.
