Stability of Phase Locking for Bidirectionally Non-Symmetric Coupled Kuramoto Oscillators in a Ring

Abstract

This paper deals with the stability of phase locking for the identical Kuramoto model, where each oscillator is influenced sinusoidally by two neighboring oscillators. By studying the model with bidirectionally non-symmetric coupling in a ring configuration, all phase-locked solutions are comprehensively delineated, and the basin of attraction for the stable phase-locked state is estimated. The stability of these phase-locked solutions is clearly established, highlighting that only the synchronized state and splay-state are stable equilibria. The crucial tools in this work are the standard linearization technique and the nonlinear analysis arguments.