Accelerating Universe with a dynamic cosmological term

Keeping in mind the current picture of an accelerating and flat Universe, some specific dynamical models of the cosmological term $\mathrm{\Lambda }$ have been selected for investigating the nature of dark energy. Connecting the free parameters of the models with the cosmic matter and vacuum energy density parameters, it is shown that the models are equivalent. Using the selected models, the present values of some of the physical parameters have been estimated, and a glimpse at the past decelerating universe has also been presented. It is observed that most of these cosmological parameters nicely agree with the values suggested by the Type Ia Supernovae and other experimental data.