  The Ekpyrotic scenario is studied in the context of some extensions of
Ho\v{r}ava-Lifshitz gravity. Some particular solutions that lead to cyclic
Hubble parameters are analyzed, where the corresponding gravitational actions
are reconstructed by using several techniques and auxiliary fields. Its
comparison with standard $F(R)$ gravity is performed. In addition, the
so-called Little Rip, a stage of the universe evolution when some bounded
systems may be dissolute, is also studied in this frame of theories.
