Numerical Study of Synchronization in the Kuramoto Model with Finite Inertia

We numerically investigate the role of inertia in the synchronization of globally coupled oscillators in the context of the nature of the synchronization transition. Using the modified Kuramoto model with an inertial term studied by Tanaka et. al., [Phys. Rev. Lett. 78, 2104 (1997)], we measure various physical quantities and determine the threshold of the coupling strength for various values of the magnitude of the inertia that each oscillator possesses. In particular, we employ a conventional analysis of finite-size eects as well as a hysteresis curve analysis. Finally, we argue for the possibility of continuous phase transitions even in the presence of inertia, for which the validity of Binder cumulant’s dip and the hysteresis curve are discussed as signatures of a discontinuous transition.