  The conditions under which synchronization is achieved for a one-dimensional
ring of identical phase oscillators with Kuramoto-like local coupling are
studied. The system is approached in the weakly coupled approximation as phase
units. Instead of global couplings, nearest-neighbor interaction is assumed.
Units are pairwise coupled by a Kuramoto term driven by their phase
differences. The system exhibits a rich set of behaviors depending on the
balance between the natural frequency of isolated units and the self-feedback.
The case of two oscillators is solved analytically, while a numerical approach
is used for $N>2$. Building from Kuramoto, the approach to synchronization,
when possible, is studied through a local complex order parameter. The system
can eventually evolve as a set of coupled local communities towards a given
phase value. However, the approach to the stationary state shows a
non-monotonous non-trivial dynamic.
