Md Sayeed Anwar, Nikita Frolov, Alexander E. Hramov, Dibakar Ghosh
{"title":"全局耦合高阶网络的自组织双稳态性","authors":"Md Sayeed Anwar, Nikita Frolov, Alexander E. Hramov, Dibakar Ghosh","doi":"arxiv-2401.02825","DOIUrl":null,"url":null,"abstract":"Self-organized bistability (SOB) stands as a critical behavior for the\nsystems delicately adjusting themselves to the brink of bistability,\ncharacterized by a first-order transition. Its essence lies in the inherent\nability of the system to undergo enduring shifts between the coexisting states,\nachieved through the self-regulation of a controlling parameter. Recently, SOB\nhas been established in a scale-free network as a recurrent transition to a\nshort-living state of global synchronization. Here, we embark on a theoretical\nexploration that extends the boundaries of the SOB concept on a higher-order\nnetwork (implicitly embedded microscopically within a simplicial complex) while\nconsidering the limitations imposed by coupling constraints. By applying\nOtt-Antonsen dimensionality reduction in the thermodynamic limit to the\nhigher-order network, we derive SOB requirements under coupling limits that are\nin good agreement with numerical simulations on systems of finite size. We use\ncontinuous synchronization diagrams and statistical data from spontaneous\nsynchronized events to demonstrate the crucial role SOB plays in initiating and\nterminating temporary synchronized events. We show that under weak coupling\nconsumption, these spontaneous occurrences closely resemble the statistical\ntraits of the epileptic brain functioning.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"11 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Self-organized bistability on globally coupled higher-order networks\",\"authors\":\"Md Sayeed Anwar, Nikita Frolov, Alexander E. Hramov, Dibakar Ghosh\",\"doi\":\"arxiv-2401.02825\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Self-organized bistability (SOB) stands as a critical behavior for the\\nsystems delicately adjusting themselves to the brink of bistability,\\ncharacterized by a first-order transition. Its essence lies in the inherent\\nability of the system to undergo enduring shifts between the coexisting states,\\nachieved through the self-regulation of a controlling parameter. Recently, SOB\\nhas been established in a scale-free network as a recurrent transition to a\\nshort-living state of global synchronization. Here, we embark on a theoretical\\nexploration that extends the boundaries of the SOB concept on a higher-order\\nnetwork (implicitly embedded microscopically within a simplicial complex) while\\nconsidering the limitations imposed by coupling constraints. By applying\\nOtt-Antonsen dimensionality reduction in the thermodynamic limit to the\\nhigher-order network, we derive SOB requirements under coupling limits that are\\nin good agreement with numerical simulations on systems of finite size. We use\\ncontinuous synchronization diagrams and statistical data from spontaneous\\nsynchronized events to demonstrate the crucial role SOB plays in initiating and\\nterminating temporary synchronized events. We show that under weak coupling\\nconsumption, these spontaneous occurrences closely resemble the statistical\\ntraits of the epileptic brain functioning.\",\"PeriodicalId\":501305,\"journal\":{\"name\":\"arXiv - PHYS - Adaptation and Self-Organizing Systems\",\"volume\":\"11 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-01-05\",\"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-2401.02825\",\"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-2401.02825","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
自组织双稳态(SOB)是系统微妙调整自身至双稳态边缘的一种关键行为,其特点是一阶转换。其本质在于系统通过控制参数的自我调节,在共存状态之间进行持久转换的内在能力。最近,SOB 在无标度网络中被确定为一种向全局同步的ort-living 状态的反复转换。在这里,我们开始了理论探索,将 SOB 概念的边界扩展到更高阶的网络(隐含地微观嵌入到一个简单复合物中),同时考虑到耦合约束所带来的限制。通过将热力学极限中的奥特-安东森降维法应用于高阶网络,我们得出了耦合限制下的 SOB 要求,这些要求与有限大小系统的数值模拟结果非常吻合。我们利用连续同步图和自发同步事件的统计数据来证明 SOB 在启动和终止临时同步事件中的关键作用。我们证明,在弱耦合消耗条件下,这些自发事件与癫痫脑功能的统计特征非常相似。
Self-organized bistability on globally coupled higher-order networks
Self-organized bistability (SOB) stands as a critical behavior for the
systems delicately adjusting themselves to the brink of bistability,
characterized by a first-order transition. Its essence lies in the inherent
ability of the system to undergo enduring shifts between the coexisting states,
achieved through the self-regulation of a controlling parameter. Recently, SOB
has been established in a scale-free network as a recurrent transition to a
short-living state of global synchronization. Here, we embark on a theoretical
exploration that extends the boundaries of the SOB concept on a higher-order
network (implicitly embedded microscopically within a simplicial complex) while
considering the limitations imposed by coupling constraints. By applying
Ott-Antonsen dimensionality reduction in the thermodynamic limit to the
higher-order network, we derive SOB requirements under coupling limits that are
in good agreement with numerical simulations on systems of finite size. We use
continuous synchronization diagrams and statistical data from spontaneous
synchronized events to demonstrate the crucial role SOB plays in initiating and
terminating temporary synchronized events. We show that under weak coupling
consumption, these spontaneous occurrences closely resemble the statistical
traits of the epileptic brain functioning.