AI 中文总结
研究有惯性的Kuramoto模型，探究单峰高斯和多峰均匀两种本征频率分布形式，发现其产生不同同步簇，导致序参量行为及同步路径不同，为惯性复杂系统集体同步动力学提供新视角。
AI 中文摘要
同步现象在自然和合成系统中普遍存在，但大多数先前研究集中在无惯性的Kuramoto模型且是在宏观层面。本研究转而考察有惯性的Kuramoto模型，分析欠阻尼动力学中由不同频率的多个同步簇间相互作用驱动而出现的单个同步簇的动力学。具体探究了单峰高斯和多峰均匀两种本征频率分布形式，发现它们产生性质不同的同步簇。这导致序参量有不同行为，同步路径也因分布类型而异。这些发现为惯性复杂系统中的集体同步动力学提供了新视角。
英文摘要
Synchronization is ubiquitous across natural and synthetic systems, yet most prior studies focus on the inertia-free Kuramoto model and do so at the macroscopic level. In this study, we instead investigate the inertial Kuramoto model and analyze the kinetics of individual synchronized clusters that emerge in the underdamped dynamics, driven by the interactions among multiple synchronized clusters with different frequencies. Specifically, we explore two forms of intrinsic frequency distribution -- unimodal Gaussian and multimodal uniform -- and show that they give rise to qualitatively different synchronized clusters: a hierarchical organization for the Gaussian distribution and a homogeneous organization for the uniform distribution. This contrast leads to qualitatively different behaviors of the order parameter: for the Gaussian distribution, it increases smoothly with increasing coupling strength, while for the uniform distribution, it grows through a series of discrete jumps that trace out the size of the Devil's staircase (DS). By resolving the kinetics at the cluster level, we further find that the route to synchronization also depends on the distribution type: with a Gaussian distribution, a single dominant cluster forms and gradually entrains the remaining oscillators, whereas with a uniform distribution, synchronization proceeds via successive cluster mergers initiated from peripheral seeds associated with the high-frequency periphery. Taken together, these findings provide a new perspective on collective synchronization dynamics in inertial complex systems.
Comments31 pages, 26 figures
