Metastability of multi-population Kuramoto-Sakaguchi oscillators

Bojun Li, Nariya Uchida
{"title":"Metastability of multi-population Kuramoto-Sakaguchi oscillators","authors":"Bojun Li, Nariya Uchida","doi":"arxiv-2405.15396","DOIUrl":null,"url":null,"abstract":"An Ott-Antonsen reduced $M$-population of Kuramoto-Sakaguchi oscillators is\ninvestigated, focusing on the influence of the phase-lag parameter $\\alpha$ on\nthe collective dynamics. For oscillator populations coupled on a ring, we\nobtained a wide variety of spatiotemporal patterns, including coherent states,\ntraveling waves, partially synchronized states, modulated states, and\nincoherent states. Back-and-forth transitions between these states are found,\nwhich suggest metastability. Linear stability analysis reveals the stable\nregions of coherent states with different winding numbers $q$. Within certain\n$\\alpha$ ranges, the system settles into stable traveling wave solutions\ndespite the coherent states also being linearly stable. For around $\\alpha\n\\approx 0.46\\pi$, the system displays the most frequent metastable transitions\nbetween coherent states and partially synchronized states, while for $\\alpha$\ncloser to $\\pi/2$, metastable transitions arise between partially synchronized\nstates and modulated states. This model captures metastable dynamics akin to\nbrain activity, offering insights into the synchronization of brain networks.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"63 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Adaptation and Self-Organizing Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2405.15396","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

Abstract

An Ott-Antonsen reduced $M$-population of Kuramoto-Sakaguchi oscillators is investigated, focusing on the influence of the phase-lag parameter $\alpha$ on the collective dynamics. For oscillator populations coupled on a ring, we obtained a wide variety of spatiotemporal patterns, including coherent states, traveling waves, partially synchronized states, modulated states, and incoherent states. Back-and-forth transitions between these states are found, which suggest metastability. Linear stability analysis reveals the stable regions of coherent states with different winding numbers $q$. Within certain $\alpha$ ranges, the system settles into stable traveling wave solutions despite the coherent states also being linearly stable. For around $\alpha \approx 0.46\pi$, the system displays the most frequent metastable transitions between coherent states and partially synchronized states, while for $\alpha$ closer to $\pi/2$, metastable transitions arise between partially synchronized states and modulated states. This model captures metastable dynamics akin to brain activity, offering insights into the synchronization of brain networks.
多群体仓本坂口振荡器的转移性
研究了仓本-坂口振荡器的奥特-安东森缩小 $M$ 群体,重点是相位滞后参数 $\alpha$ 对集体动力学的影响。对于耦合在环上的振荡器群,我们获得了各种各样的时空模式,包括相干态、行波、部分同步态、调制态和非相干态。我们还发现了这些状态之间的来回转换,这表明了它们的可转移性。线性稳定性分析揭示了不同绕组数 $q$ 相干态的稳定区域。在一定的$\alpha$范围内,尽管相干态也是线性稳定的,但系统会进入稳定的行波解。在大约 $\alpha\approx 0.46\pi$ 的范围内,系统在相干态和部分同步态之间表现出最频繁的可转移性,而当 $\alpha$ 接近 $\pi/2$ 时,可转移性会出现在部分同步态和调制态之间。这个模型捕捉到了类似大脑活动的可变动态,为研究大脑网络的同步化提供了启示。
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
自引率
0.00%
发文量
0
×
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