标题： 自同步振荡器的Kuramoto模型的线性重述 显示英文标题

标题： A linear reformulation of the Kuramoto model of self-synchronizing oscillators

摘要： 本文介绍了一种Kuramoto模型的线性重述，该模型描述了一个全局耦合振荡器系统中的自同步相变，这些振荡器通常具有不同的特征频率。 重述后的模型提供了一个替代的连贯框架，通过该框架可以解析地处理原Kuramoto分析无法解决的同步问题。 它允许显式求解同步序参数和临界点，包括1) 具有有限数量振荡器的系统的完全相位锁定过渡（与原Kuramoto模型不同，原模型仅在平均场极限下可解），以及2) 一类新的连续体系统。 它还使得能够探测系统向稳态移动时的动力学行为。 尽管本文讨论的系统仅限于全局耦合系统，但由线性重述引入的新形式也适用于解决具有局部或非对称耦合的系统。 显示英文摘要

摘要： The present paper introduces a linear reformulation of the Kuramoto model describing a self-synchronizing phase transition in a system of globally coupled oscillators that in general have different characteristic frequencies. The reformulated model provides an alternative coherent framework through which one can analytically tackle synchronization problems that are not amenable to the original Kuramoto analysis. It allows one to solve explicitly for the synchronization order parameter and the critical point of 1) the full phase-locking transition for a system with a finite number of oscillators (unlike the original Kuramoto model, which is solvable implicitly only in the mean-field limit) and 2) a new class of continuum systems. It also makes it possible to probe the system's dynamics as it moves towards a steady state. While discussion in this paper is restricted to systems with global coupling, the new formalism introduced by the linear reformulation also lends itself to solving systems that exhibit local or asymmetric coupling.