Theoretical Analysis and Numerical Verification of Stability in Weighted Kuramoto Models

This paper systematically studies the theoretical advancements and engineering applications of the Kuramoto oscillator model in the synchronization dynamics of complex networks. As a classical dynamical model, the Kuramoto model is widely utilized to uncover collective oscillatory behaviors and synchronization mechanisms in complex systems, demonstrating significant implications for the synchronization phenomena observed in domains such as biological rhythms, neural networks, and chemical oscillations. Firstly, this paper provides a comprehensive review of the core structure of the Kuramoto equations, the historical progression of its development, and the critical coupling strength Kc necessary for synchronization. Building upon this foundation, this article proposes a weighted network Kuramoto model that considers mass disparity, and theoretically derives the constraints of quality deviation on system synchronization behavior. It proves that under specific initial conditions, the synchronization threshold of the model exhibits robustness against mass perturbations. Numerical simulations further verify that the model displays remarkable synchronization patterns under restricted coupling strengths K , while the impact of mass disparity on synchronization properties remains limited. This research offers a novel theoretical framework for elucidating the synchronization behavior. of complex network systems and holds significant practical relevance for applications in power system stability analysis, neural dynamics modeling, and distributed cooperative control in engineering contexts.