Sufficient conditions for asymptotic phase-locking to the generalized Kuramoto model

<p style='text-indent:20px;'>In this paper, we introduce a generalized Kuramoto model and provide several sufficient conditions leading to asymptotic phase-locking. The proposed incorporates relativistic type models which can be derived from the Cucker-Smale (RCS) on unit sphere via suitable approximations. For phase-locking, present frameworks complete synchronization in terms of initial data system parameters. model, show that it reduces finite time interval, as speed light tends infinity. Moreover, for some admissible data, nonrelativistic limit made uniformly time. We also numerical examples two approximations compare them with analytical results.</p>