Dynamics of Tachyon and Phantom Field beyond the Inverse Square Potentials

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We investigate the cosmological evolution of the tachyon and phantom-tachyon scalar field by considering the potential parameter Γ(=V V"/V'²) as a function of another potential parameter λ(=V'κV³/²), 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 Γ(λ) equals 3/2 for one or some values of λ* as well as the parameter λ* 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.