  We perform a detailed phase-space analysis of a class of k-essence cosmology.
We find the critical points can be divided into three classes: points unstable
but the model stable, both points and the model stable, points stable but the
model unstable. Like the case of points unstable but the model stable, the case
of points stable but the model unstable is not relevant from a cosmological
point of view, though they can be late-time attractors for the universe. So in
order to study the possible final state of the universe, it is important to
investigate not only the stability of the critical points but also the
stability of the model. The case of both points and the model stable can
further be divided into two classes: points only presenting decelerating phases
and points at which all decelerating, constant-speed, and accelerating phases
can appear; the final state of the universe dependents on the potential.
