论文标题
库拉莫托模型中的同步条件及其与eminorm的关系
Synchronization conditions in the Kuramoto model and their relationship to seminorms
论文作者
论文摘要
在本文中，我们解决了有关库拉莫托模型中耦合振荡器同步的两个问题，并全都耦合。在第一部分中，我们在凸几何形状中使用一些经典结果来证明频率集的大小支持稳定的，相位锁定的解决方案的存在，并表明这种频率的集合可以通过eminorm表示，我们称之为kuramoto norm。在第二部分中，我们使用极端顺序统计的一些想法来计算非常通用频率分布的同步概率的上限和下限。我们这样做是通过准确计算等同于库拉莫托规范的数量的极端价值分布。
In this paper we address two questions about the synchronization of coupled oscillators in the Kuramoto model with all-to-all coupling. In the first part we use some classical results in convex geometry to prove bounds on the size of the frequency set supporting the existence of stable, phase locked solutions and show that the set of such frequencies can be expressed by a seminorm which we call the Kuramoto norm. In the second part we use some ideas from extreme order statistics to compute upper and lower bounds on the probability of synchronization for very general frequency distributions. We do so by computing exactly the limiting extreme value distribution of a quantity that is equivalent to the Kuramoto norm.
