Local and Grobal Self-Entrainments in Oscillator Lattices

By computer simulations of an active rotator model, it is found that 1-, 2- and 3-dimensional oscillator lattices with distributed natural frequencies exhibit peculiar clustering patterns due to local entrainment. A simple theory suggest that some of such self-entrained clusters may or may not develop into macroscopic size depending on system dimension, and this fact consistently explains our numerically obtained order parameter curves.