Stability of Phase Locking for Bidirectionally Non-Symmetric Coupled Kuramoto Oscillators in a Ring (Journal of Nonlinear Modeling and Analysis, 2025)
This paper deals with the stability of phase locking for the identicalKuramoto model, where each oscillator is influenced sinusoidally by two neighboring oscillators. By studying the model with bidirectionally non-symmetriccoupling in a ring configuration, all phase-locked solutions are comprehensivelydelineated, 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 techniqueand the nonlinear analysis arguments.
Keywords: Coupled oscillators; stability; phase locking; synchronization.