标题： 求解自同步的有限群体全局耦合振荡器的Kuramoto模型 显示英文标题

标题： Solving the Kuramoto model of a self-synchronizing, finite population of globally coupled oscillators

摘要： 本信件介绍了一个线性模型，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固有频率。 此线性模型在稳态条件下被证明可以映射到广泛研究的 Kuramoto 同步模型，并且通过与 Kuramoto 模型不同的方法，可以求解相变发生的临界点。 然而，与需要处于平均场极限（即振荡器数量趋于无穷大）才能在稳态条件下隐式求解序参数的 Kuramoto 模型不同，此线性模型为具有任意数量振荡器的系统提供了序参数的显式解析解，并允许研究系统向稳态移动时的动力学行为。 尽管本信件的讨论仅限于全局耦合系统，但该线性模型为进一步研究局部和/或非对称耦合方案提供了便利的起点。 显示英文摘要

摘要： The present letter introduces a linear model describing a self-synchronizing phase transition in a system of globally coupled oscillators that in general have different intrinsic frequencies. This linear model is shown in the steady-state regime to map onto the much-studied Kuramoto synchronization model and, through a different approach from the Kuramoto model, can be solved for the critical point at which the phase transition occurs. However, unlike the Kuramoto model, which requires that one be in the mean-field limit (in which the number of oscillators go to infinity) in order to be solvable implicitly for the order parameter in the steady-state regime, this linear model yields an explicit analytic solution for the order parameter of a system with any number of oscillators and allows one to probe the system's dynamics as it moves towards a steady state. While discussion in this letter is restricted to systems with global coupling, the linear model provides a convenient springboard for further studies involving local and/or asymmetric coupling schemes.