  We investigate the cosmological evolution of the tachyon and phantom-tachyon
scalar field by considering the potential parameter $\Gamma$($=\frac{V
V"}{V'^2}$) as a function of another potential parameter
$\lambda$($=\frac{V'}{\kappa V^{3/2}}$), which correspondingly extends the
analysis of the evolution of our universe from two-dimensional autonomous
dynamical system to the three-dimension. It allows us to investigate the more
general situation where the potential is not restricted to inverse square
potential and .One result is that, apart from the inverse square potential,
there are a large number of potentials which can give the scaling and dominant
solution when the function $\Gamma(\lambda)$ equals $3/2$ for one or some
values of $\lambda_{*}$ as well as the parameter $\lambda_{*}$ satisfies
condition Eq.(18) or Eq.(19). We also find that for a class of different
potentials the dynamics evolution of the universe are actually the same and
therefore undistinguishable.
