We investigate evolutional paths of an extended quintessence with a non-minimally coupled phantom scalar field \psi to the Ricci curvature .
The dynamical system methods are used to investigate typical regimes of dynamics at the late time .
We demonstrate that there are two generic types of evolutional scenarios which approach the attractor ( a focus or a node type critical point ) in the phase space : the quasi-oscillatory and monotonic trajectories approach to the attractor which represents the FRW model with the cosmological constant .
We demonstrate that dynamical system admits invariant two-dimensional submanifold and discussion that which cosmological scenario is realized depends on behavior of the system on the phase plane ( \psi, \psi ^ { \prime } ) .
We formulate simple conditions on the value of coupling constant \xi for which trajectories tend to the focus in the phase plane and hence damping oscillations around the mysterious value w = -1 .
We describe this condition in terms of slow-roll parameters calculated at the critical point .
We discover that the generic trajectories in the focus-attractor scenario come from the unstable node .
It is also investigated the exact form of the parametrization of the equation of state parameter w ( z ) ( directly determined from dynamics ) which assumes a different form for both scenarios .