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We investigate the cosmological evolution of the tachyon and phantom-tachyonscalar field by considering the potential parameter $\Gamma$($=\frac{VV"}{V'^2}$) as a function of another potential parameter$\lambda$($=\frac{V'}{\kappa V^{3/2}}$), which correspondingly extends theanalysis of the evolution of our universe from two-dimensional autonomousdynamical system to the three-dimension. It allows us to investigate the moregeneral situation where the potential is not restricted to inverse squarepotential and .One result is that, apart from the inverse square potential,there are a large number of potentials which can give the scaling and dominantsolution when the function $\Gamma(\lambda)$ equals $3/2$ for one or somevalues of $\lambda_{*}$ as well as the parameter $\lambda_{*}$ satisfiescondition Eq.(18) or Eq.(19). We also find that for a class of differentpotentials the dynamics evolution of the universe are actually the same andtherefore undistinguishable.

Dynamics of Tachyon and Phantom Field beyond the Inverse Square Potentials