  In this work we develop a general phenomenological model of the Cyclic
Universe. We construct periodic scale factor a(t) from the requirements of the
periodicity of a(t) with no singular behavior at the turning points t_\alpha
and t_\omega and the requirement that a unique analytical form of the Hubble
function H(z) can be derived from the Hubble function H(t) to fit the data on
H(z). We obtain two versions of a(t) called Model A and Model C. Hubble data
select Model A. With the analytical forms of the Hubble functions H(t) and H(z)
known we calculate the deceleration parameters q(t) and q(z) to study the
acceleration-deceleration transitions during the expansion phase. We find that
the initial acceleration at t_\alpha=0 transits at t_{ad1}=3.313x10^{-38}s into
deceleration period that transits at t_{da}=6.713 Gyr to the present period of
acceleration. The present acceleration shall end in a transition to the final
deceleration at t_{ad2}=38.140 Gyr. The expansion period lasts 60.586 Gyr. The
complete cycle period is T=121.172 Gyr. We use the deceleration parameters q(z)
and q(t) to solve the Friedmann equations for the energy densities of Dark
Energy \Omega_0 and Dark Matter \Omega_M to describe their evolutions over a
large range of z and t. We show that in the Model A the curvature density
\Omega_c(z) evolves from a flat Universe in the early times to a curves anti
de-Sitter spacetime today. There is no Standard Model Inflation in the Model A.
