Complete and Partial Synchronization of Two-Group and Three-Group Kuramoto Oscillators

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-07-09 DOI:10.1137/23m1586227

Shih-Hsin Chen, Chun-Hsiung Hsia, Ting-Yang Hsiao

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Abstract

SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 3, Page 1720-1765, September 2024.
Abstract.This paper is to investigate synchronization theories of a two-group Kuramoto model and a three-group Kuramoto model. In the settings of these models, every oscillator directly interacts with each other in the same group. In each group, only one oscillator directly interacts with one oscillator in another group. We prove that if the coupling strength is large and the initial configuration of each group is confined to a sector with the arc length less than [math], then all oscillators achieve a complete frequency synchronization asymptotically. We emphasize that there is no need to impose any initial condition on the connection between different groups. If, in addition, the natural frequencies in one group are the same, then partial phase synchronization occurs. Moreover, if all natural frequencies are identical, we prove that all oscillators either achieve a complete phase synchronization asymptotically or tend to a bipolar phase-locking state. We also provide several numerical simulations to support the main results.

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两组和三组仓本振荡器的完全同步和部分同步

SIAM 应用动力系统学报，第 23 卷第 3 期，第 1720-1765 页，2024 年 9 月。摘要：本文主要研究两组仓本模型和三组仓本模型的同步理论。在这些模型的设置中，每个振子在同一组中直接相互作用。在每一组中，只有一个振子与另一组中的一个振子直接相互作用。我们证明，如果耦合强度很大，并且每个振子组的初始配置被限制在一个弧长小于 [math] 的扇形区域内，那么所有振子都会渐近地实现完全的频率同步。我们强调，不同振子组之间的连接无需施加任何初始条件。此外，如果一组振子的固有频率相同，则会出现部分相位同步。此外，如果所有固有频率相同，我们证明所有振荡器要么渐近地实现完全相位同步，要么趋向于双极锁相状态。我们还提供了一些数值模拟来支持主要结果。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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