  We study the cosmological evolutions of the equation of state (EoS) for the
universe in the homogeneous and isotropic
Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) space-time. In particular, we
reconstruct the cyclic universes by using the Weierstrass and Jacobian elliptic
functions. It is explicitly illustrated that in several models the universe
always stays in the non-phantom (quintessence) phase, whereas there also exist
models in which the crossing of the phantom divide can be realized in the
reconstructed cyclic universes.
