Counting Equilibria of the Kuramoto Model Using Birationally Invariant Intersection Index
Counting Equilibria of the Kuramoto Model Using Birationally Invariant Intersection Index
复制标题
使用双有理不变交集指数计算 Kuramoto 模型的平衡
DOI：
10.1137/17m1145665
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
D. Mehta
中科院分区：
文献类型：
--
作者：
Tianran Chen;Robert Davis;D. Mehta
相互连接的振子网络中的同步是一种迷人的现象，它自然地出现在科学和工程的许多独立领域中。大量的工作致力于理解给定网络上所有可能的同步配置。在这种情况下，一个关键问题是确定此类配置的总数。通过一种代数公式，对于树图和循环图，我们利用环面簇上有理函数系的双有理不变相交指数给出了这个数的一个上界。
Synchronization in networks of interconnected oscillators is a fascinating phenomenon that appear naturally in many independent fields of science and engineering. A substantial amount of work has been devoted to understanding all possible synchronization configurations on a given network. In this setting, a key problem is to determine the total number of such configurations. Through an algebraic formulation, for tree and cycle graphs, we provide an upper bound on this number using the birationally invariant intersection index of a system of rational functions on a toric variety.