Abstract
In this paper, we consider the dilatonic dark energy model and its phantom model. Based on the dilatonic (phantom) model, we take the potential of dilaton field of the form [1+(σ-A)2]e-Bσ which seems to connect with ideas from M-theory, and analyze the sufficient condition for the existence of attractor solution. We find that the behavior of the attractor is not sensitive to the initial condition, thus the fine-tuning problem is alleviated. By numerical analysis, we investigate the asymptotic behavior of the attractor, which corresponds to an equation of state ω = -1 and a cosmic density parameter Ωσ = 1.
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