Hamiltonian control to desynchronize Kuramoto oscillators with higher-order interactions.

IF 2.4 3区 物理与天体物理 Q1 Mathematics
Martin Moriamé, Maxime Lucas, Timoteo Carletti
{"title":"Hamiltonian control to desynchronize Kuramoto oscillators with higher-order interactions.","authors":"Martin Moriamé, Maxime Lucas, Timoteo Carletti","doi":"10.1103/PhysRevE.111.044307","DOIUrl":null,"url":null,"abstract":"<p><p>Synchronization is a ubiquitous phenomenon in nature. Although it is necessary for the functioning of many systems, too much synchronization can also be detrimental; e.g., (partially) synchronized brain patterns support high-level cognitive processes and bodily control, but hypersynchronization can lead to epileptic seizures and tremors, as in neurodegenerative conditions such as Parkinson's disease. Consequently, a critical research question is how to develop effective pinning control methods capable to reduce or modulate synchronization as needed. Although such methods exist to control pairwise-coupled oscillators, and pinning control for synchronization has been developed in higher-order systems in recent years, there are no desynchronizing control methods for higher-order interactions, despite the increasing evidence of their relevant role in brain dynamics. In this work, we fill this gap by proposing a generalized control method designed to desynchronize Kuramoto oscillators connected through higher-order interactions. Our method embeds a higher-order Kuramoto model into a suitable Hamiltonian flow, and builds upon previous work in Hamiltonian control theory to analytically construct a feedback control mechanism. We numerically show that the proposed method effectively prevents synchronization in synthetic and empirical higher-order networks. Although our findings indicate that pairwise contributions in the feedback loop are often sufficient, the higher-order generalization becomes crucial when pairwise coupling is weak. Finally, we explore the minimum number of controlled nodes required to fully desynchronize oscillators coupled via an all-to-all hypergraph.</p>","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"111 4-1","pages":"044307"},"PeriodicalIF":2.4000,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical review. E","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/PhysRevE.111.044307","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0

Abstract

Synchronization is a ubiquitous phenomenon in nature. Although it is necessary for the functioning of many systems, too much synchronization can also be detrimental; e.g., (partially) synchronized brain patterns support high-level cognitive processes and bodily control, but hypersynchronization can lead to epileptic seizures and tremors, as in neurodegenerative conditions such as Parkinson's disease. Consequently, a critical research question is how to develop effective pinning control methods capable to reduce or modulate synchronization as needed. Although such methods exist to control pairwise-coupled oscillators, and pinning control for synchronization has been developed in higher-order systems in recent years, there are no desynchronizing control methods for higher-order interactions, despite the increasing evidence of their relevant role in brain dynamics. In this work, we fill this gap by proposing a generalized control method designed to desynchronize Kuramoto oscillators connected through higher-order interactions. Our method embeds a higher-order Kuramoto model into a suitable Hamiltonian flow, and builds upon previous work in Hamiltonian control theory to analytically construct a feedback control mechanism. We numerically show that the proposed method effectively prevents synchronization in synthetic and empirical higher-order networks. Although our findings indicate that pairwise contributions in the feedback loop are often sufficient, the higher-order generalization becomes crucial when pairwise coupling is weak. Finally, we explore the minimum number of controlled nodes required to fully desynchronize oscillators coupled via an all-to-all hypergraph.

具有高阶相互作用的Kuramoto振子去同步的hamilton控制。
同步是自然界中普遍存在的现象。虽然这对许多系统的运作是必要的,但过多的同步也可能是有害的;例如,(部分)同步的大脑模式支持高级认知过程和身体控制,但过度同步可导致癫痫发作和震颤,如帕金森氏病等神经退行性疾病。因此,一个关键的研究问题是如何开发有效的钉住控制方法,能够根据需要减少或调制同步。尽管存在这样的方法来控制成对耦合振荡器,并且近年来在高阶系统中开发了同步的钉住控制,但尽管越来越多的证据表明它们在脑动力学中的相关作用,但还没有高阶相互作用的去同步控制方法。在这项工作中,我们提出了一种通用的控制方法来消除通过高阶相互作用连接的Kuramoto振荡器的同步,从而填补了这一空白。我们的方法将高阶Kuramoto模型嵌入到合适的哈密顿流中,并在哈密顿控制理论的基础上解析构建反馈控制机制。数值结果表明,该方法有效地防止了综合高阶网络和经验高阶网络的同步。尽管我们的研究结果表明,反馈回路中的成对贡献通常是足够的,但当成对耦合较弱时,高阶泛化变得至关重要。最后,我们探讨了通过全对全超图耦合的振荡器完全去同步所需的最小控制节点数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
Physical review. E
Physical review. E 物理-物理:流体与等离子体
CiteScore
4.60
自引率
16.70%
发文量
0
审稿时长
3.3 months
期刊介绍: Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信