{"title":"多群体仓本坂口振荡器的转移性","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":"{\"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}","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}
Metastability of multi-population Kuramoto-Sakaguchi oscillators
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.