任意维网络振子的惯性同步
Inertial synchronization of networked oscillators in arbitrary dimensions
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中文总结 AI 辅助
该研究提出任意维惯性Kuramoto模型，发现惯性可将同步转变从连续变为不连续，滞后与惯性及维数奇偶性相关，经数值模拟验证，确立惯性为高维集体动力学关键要素。
中文摘要 AI 辅助
Kuramoto模型是研究相互作用振子同步的经典框架，已被推广至任意维以描述群集、 flock（蜂群）及多维观点动力学。但现有模型未考虑惯性这一可增强信息传播与集体响应的关键机制。本文提出并分析了任意维的惯性Kuramoto模型，发现惯性从根本上改变了同步转变的性质，诱导出从连续到不连续行为的交叉，滞后的出现明确依赖于惯性和维数的奇偶性。大量数值模拟验证了该分析理论，这些结果确立了惯性是高维集体动力学的关键要素，并揭示了同步现象中一种新颖的普适结构。
英文摘要
The Kuramoto model provides a paradigmatic framework for studying synchronization of interacting oscillators, and has been generalized to arbitrary dimensions to describe swarms, flocks and multi-dimensional opinion dynamics. Yet, existing formulations neglect inertia, a key mechanism known to enhance information propagation and collective responsiveness. Here, we introduce and analyze an inertial Kuramoto model in arbitrary dimensions. We show that inertia fundamentally alters the nature of the synchronization transition, inducing a crossover from continuous to discontinuous behavior, with the onset of hysteresis depending explicitly on both inertia and dimensionality parity. Our analytical theory is supported by extensive numerical simulations. These results establish inertia as a crucial ingredient of high-dimensional collective dynamics and reveal a novel universal structure in synchronization phenomena.
