  In this paper I examine the phase space dynamics in the framework of
Non-Projectable Ho\v{r}ava-Lifshitz bouncing cosmologies. By considering a
closed Friedmann-Lema\^itre-Robertson-Walker (FLRW) geometry, the first
integral contains a correction term that leads to nonsingular metastable
bounces in the early evolution of the universe. The matter content of the model
is a massive conformally coupled scalar field, dust and radiation. A
nonvanishing cosmological constant connected to a de Sitter attractor in the
phase space is also assumed. In narrow windows of the parameter space, labeled
by an integer $n\geq 2$, nonlinear resonance phenomena may destroy the KAM tori
that trap the scalar field, leading to an exit to the de Sitter attractor. As a
consequence nonlinear resonance imposes constraints on the parameters and in
the initial configurations of the models so that an accelerated expansion may
be realized.
