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We constrain two dynamical dark energy models that are parametrized by thelogarithm form of $w(z)=w_{0}+w_{1}\left(\frac{\ln (2+z)}{1+z}-\ln 2\right)$and the oscillating form of$w(z)=w_{0}+w_{1}\left(\frac{\sin(1+z)}{1+z}-\sin(1)\right)$. Comparing withthe Chevallier-Polarski-Linder (CPL) model, the two parametrizations for darkenergy can explore the whole evolution history of the universe properly. Usingthe current mainstream observational data including the cosmic microwavebackground data and the baryon acoustic oscillation data as well as the type Iasupernovae data, we perform the $\chi^2$ statistic analysis to global fit thesemodels, finding that the logarithm parametrization and the oscillatingparametrization 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 thecosmological constraints on the total mass of active neutrinos. We find thatthe dark energy properties could significantly change the fitting results ofneutrino mass. Looser constraints on $\sum m_{\nu}$ are obtained in thelogarithm and oscillating models than those derived in the CPL model.Consideration of the possible mass ordering of neutrinos reveals that the moststringent constraint on $\sum m_{\nu}$ appears in the degenerate hierarchycase.

Constraining neutrino mass in dynamical dark energy cosmologies with the logarithm parametrization and the oscillating parametrization