EMERGENCE OF PHASE-LOCKED STATES FOR THE KURAMOTO MODEL IN A LARGE COUPLING REGIME
EMERGENCE OF PHASE-LOCKED STATES FOR THE KURAMOTO MODEL IN A LARGE COUPLING REGIME
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DOI：
10.4310/cms.2016.v14.n4.a10
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发表时间：
2016-01-01
影响因子：
1
通讯作者：
Ryoo, Sang Woo
中科院分区：
文献类型：
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作者：
Ha, Seung-Yeal;Kim, Hwa Kil;Ryoo, Sang Woo
我们研究了有限维仓本模型在大耦合区中从非锁相态的一般初始组态中锁相态的出现。在物理学和工程学的文献中，经常有人认为，在大耦合区域中，对于一般的初始组态，完全同步可能发生。这些论点通常基于数值模拟的结果。不幸的是，这个看似合理的方案还没有完全验证严格的数学论证，虽然有几个部分结果可用于有限的初始配置类。在本文中，我们提供了一个充分的框架，完全同步从一个通用的初始配置在一个大的耦合制度。我们的分析依赖于仓本模型的梯度流结构和相配置的一致有界性。
We study the emergence of phase-locked states to the finite-dimensional Kuramoto model from generic initial configurations which are not phase-locked states in a large coupling regime. In the literature of physics and engineering, it has often been argued that complete synchronization may occur for a generic initial configuration in a large coupling regime. Such arguments are generally based on the results of numerical simulations. Unfortunately, this plausible scenario has not been completely verified by rigorous mathematical arguments, although there are several partial results available for a restricted class of initial configurations. In this paper, we provide a sufficient framework for complete synchronization from a generic initial configuration in a large coupling regime. Our analysis depends on the gradient flow structure of the Kuramoto model and the uniform boundedness of the phase configuration.