本文系统研究了Kuramoto振子模型在复杂网络同步动力学中的理论拓展与工程应用。作为经典动力学模型, Kuramoto模型广泛用于揭示复杂系统中的集体振荡行为及其同步机制, 对生物节律、神经网络和化学振荡等领域的同步现象具有重要意义。首先, 本文系统回顾了Kuramoto方程的核心结构、发展历程以及临界耦合强度Ke的必要条件。在此基础上, 本文提出了考虑质量偏差的加权网络 Kuramoto模型, 并从理论上推导出质量偏差对系统同步行为的约束条件, 证明在特定初始条件下, 模型的同步阈值对质量扰动具有鲁棒性。通过数值模拟验证, 该模型在耦合强度K的限制下展现出显著的同步特性, 且质量偏差对同步特性的影响有限。本研究为揭示复杂网 络系统的同步行为提供了新的理论框架, 并在电力系统稳定性分析、神经动力学建模和分布式协同控制等实际工程应用中具有重要意义。

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.