Behavior of circular chains of nonlinear oscillators with Kuramoto-like local coupling

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