Discontinuous phase transition in the Kuramoto model with asymmetric dynamic interaction.

Abstract

We investigate the critical behavior of the modified Kuramoto model with an asymmetric dynamic interaction which has been proposed to explain the difference between the synchronized frequency and the average intrinsic frequency. We find that the discontinuous phase transition arises when oscillators interact only with other oscillators whose phases are ahead. From the comparison with the conventional Kuramoto model in which the interaction possesses phase reflection symmetry, we conclude that the dynamical symmetry breaking and the dynamic change in interaction structure play important roles in changing the transition nature from continuous to discontinuous ones.