  Based on dilatonic dark energy model, we consider two cases: dilaton field
with positive kinetic energy(coupled quintessence) and with negative kinetic
energy(phantom). In the two cases, we investigate the existence of attractor
solutions which correspond to an equation of state parameter $\omega=-1$ and a
cosmic density parameter $\Omega_\sigma=1$. We find that the coupled term
between matter and dilaton can't affect the existence of attractor solutions.
In the Mexican hat potential, the attractor behaviors, the evolution of state
parameter $\omega$ and cosmic density parameter $\Omega$, are shown
mathematically. Finally, we show the effect of coupling term on the evolution
of $X(\frac{\sigma}{\sigma_0})$ and $Y(\frac{\dot{\sigma}}{\sigma^2_0})$ with
respect to $N(lna)$ numerically.
