  We propose a generalized Kuramoto model with relativistic effects and
investigate emergent asymptotic behaviors. The proposed generalized Kuramoto
model incorporates relativistic Kuramoto(RK) type models which can be derived
from the relativistic Cucker-Smale (RCS) on the unit sphere under suitable
approximations. We present several sufficient frameworks leading to complete
synchronization in terms of initial data and system parameters. For the
relativistic Kuramoto model, we show that it can be reduced to the Kuramoto
model in any finite time interval in a non-relativistic limit. We also provide
several numerical examples for two approximations of the relativistic Kuramoto
model, and compare them with analytical results.
