This paper studies phantom linear scalar field （LSF） and phantom non-linear Born-Infeld （NLBI） scalar field with square potential of the form V（Ф） =1/2m^2Ф^2. The equation of state parameter w（z）, and evolution of scale factor a（t） in both phantom LSF and phantom NLBI scalar model are explored. The age of universe Hot and the transition redshift Z are obtained. The Gold data set of 157-SN-Ia is used to constrain parameters of the two models by numerical calculation. The phantom LSF is slightly better than the phantom NLBI type scalar field model for a large m. Although a smaller m corresponding to a slower rolling of field Ф better fits the observation data, the difference between phantom NLBI scalar field and phantom LSF is not distinct in this case.
The dilaton in Weyl-Scale induced gravitational theory is regarded as a candidate of dark energy. When the potential of dilaton field is taken as the form Wσ ＋ σ^2e^-βσ2, that there exist attractor solutions to the canonical dilatonic dark energy model and the phontam model, and these attractors correspond to an equation of state ω = -1 and a cosmic density parameter Ωσ = 1, which are important features for a dark energy model and can fit with the current observations. We find a sufficient condition of the existence of a late time de Sitter attractor. The attractor behaviors, the evolutions of the state parameter ω and the cosmic density parameter Ω, the evolution of X （σ/σ0） and Y （σ/σ0^2） with respect to N（ln a）are shown numerically.
