复合仓本模型中弱耦合的同步性

arXiv - PHYS - Adaptation and Self-Organizing Systems Pub Date : 2024-04-28 DOI:arxiv-2404.19637

Moritz Thümler, Shesha G. M. Srinivas, Malte Schröder, Marc Timme

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引用次数: 0

摘要

我们提出了从实变到复变的有限大小仓本模型，并对其集体动力学进行了分析。对于强耦合，同步性是通过构成吸引子的锁定状态出现的，就像对于实变系统一样。然而，当耦合强度 $K$ 低于向经典文本{相位锁定}过渡的 $K^{(\text{pl})}$ 时，同步性以文本{复数锁定状态}的形式持续存在。稳定的复数锁相态表明在有变数模型中存在一个平均频率为零的锁相子群，它们的虚部有助于确定哪些单元组成了这个子群。我们发现了在K'本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Synchrony for weak coupling in the complexified Kuramoto model

We present the finite-size Kuramoto model analytically continued from real to complex variables and analyze its collective dynamics. For strong coupling, synchrony appears through locked states that constitute attractors, as for the real-variable system. However, synchrony persists in the form of \textit{complex locked states} for coupling strengths $K$ below the transition $K^{(\text{pl})}$ to classical \textit{phase locking}. Stable complex locked states indicate a locked sub-population of zero mean frequency in the real-variable model and their imaginary parts help identifying which units comprise that sub-population. We uncover a second transition at $K'

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arXiv - PHYS - Adaptation and Self-Organizing Systems

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