We introduce a set of two-parameter models for the dark energy equation of state ( EOS ) w ( z ) to investigate time-varying dark energy .
The models are classified into two types according to their boundary behaviors at the redshift z = ( 0 , \infty ) and their local extremum properties .
A joint analysis based on four observations ( SNe + BAO + CMB + H _ { 0 } ) is carried out to constrain all the models .
It is shown that all models get almost the same \chi ^ { 2 } _ { min } \simeq 469 and the cosmological parameters ( \Omega _ { M } ,h, \Omega _ { b } h ^ { 2 } ) with the best-fit results ( 0.28 , 0.70 , 2.24 ) , although the constraint results on two parameters ( w _ { 0 } ,w _ { 1 } ) and the allowed regions for the EOS w ( z ) are sensitive to different models and a given extra model parameter .
For three of Type I models which have similar functional behaviors with the so-called CPL model , the constrained two parameters w _ { 0 } and w _ { 1 } have negative correlation and are compatible with the ones in CPL model , and the allowed regions of w ( z ) get a narrow node at z \sim 0.2 .
The best-fit results from the most stringent constraints in Model Ia give ( w _ { 0 } ,w _ { 1 } ) = ( -0.96 ^ { +0.26 } _ { -0.21 } , -0.12 ^ { +0.61 } _ { -0.89 } ) which may compare with the best-fit results ( w _ { 0 } ,w _ { 1 } ) = ( -0.97 ^ { +0.22 } _ { -0.18 } , -0.15 ^ { +0.85 } _ { -1.33 } ) in the CPL model .
For four of Type II models which have logarithmic function forms and an extremum point , the allowed regions of w ( z ) are found to be sensitive to different models and a given extra parameter .
It is interesting to obtain two models in which two parameters w _ { 0 } and w _ { 1 } are strongly correlative and appropriately reduced to one parameter by a linear relation w _ { 1 } \propto ( 1 + w _ { 0 } ) .