Dilaton Coupled Quintessence Model in the $\omega-\omega'$ Plane

In this paper, we regard dilaton in Weyl-scaled induced gravitational theory as a coupled quintessence. Based on this consideration, we investigate the dilaton coupled quintessence(DCQ) model in $\omega-\omega'$ plane, which is defined by the equation of state parameter for the dark energy and its derivative with respect to $N$(the logarithm of the scale factor $a$). We find the scalar field equation of motion in $\omega-\omega'$ plane, and show mathematically the property of attractor solutions which correspond to $\omega_\sigma\sim-1$, $\Omega_\sigma=1$. Finally, we find that our model is a tracking one which belongs to "freezing" type model classified in $\omega-\omega'$ plane.