标题： 环形振荡器的临界耦合的解析确定 显示英文标题

标题： Analytic Determination of the Critical Coupling for Oscillators in a Ring

摘要： 我们研究了一个具有双向最近邻耦合的耦合振子模型，该模型具有周期性边界条件。 我们证明，稳定的相位锁定解由主要聚类之间的边界振子决定，这些聚类在完全同步阶段合并形成一个包含所有振子的大聚类。 我们能够定位这四个振子以及完全同步阶段附近主要聚类的大小，我们证明这仅取决于初始频率的集合。 使用此处提出的方法，我们能够获得完全同步状态发生的临界耦合的解析形式。 显示英文摘要

摘要： We study a model of coupled oscillators with bidirectional first nearest neighbours coupling with periodic boundary conditions. We show that a stable phase-locked solution is decided by the oscillators at the borders between the major clusters, which merge to form a larger one of all oscillators at the stage of complete synchronization. We are able to locate these four oscillators as well as the size of major clusters in the vicinity of the stage of full synchronization which we show to depend only on the set of initial frequencies. Using the method presented here, we are able to obtain an analytic form of the critical coupling, at which the complete synchronization state occurs.