We constrain two dynamical dark energy models that are parametrized by the logarithm form of
and the oscillating form of
. Comparing with the Chevallier-Polarski-Linder (CPL) model, the two parametrizations for dark energy can explore the whole evolution history of the universe properly. Using the current mainstream observational data including the cosmic microwave background data and the baryon acoustic oscillation data as well as the type Ia supernovae data, we perform the
X2 statistic analysis to global fit these models, finding that the logarithm parametrization and the oscillating parameterization are almost as well as the CPL scenario in fitting these data. We make a comparison for the impacts of the dynamical dark energy on the cosmological constraints on the total mass of active neutrinos. We find that the logarithm parametrization and the oscillating parameterization can increase the fitting values of Σ
mv. Looser constraints on Σ
mv are obtained in the logarithm and oscillating models than those derived in the CPL model. Consideration of the possible mass ordering of neutrinos reveals that the most stringent constraint on Σ
mv appears in the degenerate hierarchy case.