{"title":"恢复延迟动力","authors":"Kenta Ohira, Toru Ohira","doi":"arxiv-2312.04848","DOIUrl":null,"url":null,"abstract":"We introduce a delay differential equation that manifests a distinctive\ndynamical behavior. Specifically, the transient dynamics of this equation\ndemonstrate a unique ``reviving\" amplitude phenomenon within certain ranges of\ndelay values. In this intriguing phenomenon, the amplitude initially decreases\ntowards a fixed point until a specific time point, after which it ultimately\ndiverges. Our analysis encompasses both analytical and numerical approaches,\nincorporating an approximation using the Lambert W function. The derived\napproximate solution effectively captures the qualitative aspects of the\nreviving dynamics across various delay values.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"12 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Reviving Delayed Dynamics\",\"authors\":\"Kenta Ohira, Toru Ohira\",\"doi\":\"arxiv-2312.04848\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We introduce a delay differential equation that manifests a distinctive\\ndynamical behavior. Specifically, the transient dynamics of this equation\\ndemonstrate a unique ``reviving\\\" amplitude phenomenon within certain ranges of\\ndelay values. In this intriguing phenomenon, the amplitude initially decreases\\ntowards a fixed point until a specific time point, after which it ultimately\\ndiverges. Our analysis encompasses both analytical and numerical approaches,\\nincorporating an approximation using the Lambert W function. The derived\\napproximate solution effectively captures the qualitative aspects of the\\nreviving dynamics across various delay values.\",\"PeriodicalId\":501305,\"journal\":{\"name\":\"arXiv - PHYS - Adaptation and Self-Organizing Systems\",\"volume\":\"12 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-12-08\",\"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-2312.04848\",\"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-2312.04848","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
我们引入了一个延迟微分方程,它表现出一种独特的动力学行为。具体来说,该方程的瞬态动力学在一定的延迟值范围内表现出独特的 "复苏 "振幅现象。在这一引人入胜的现象中,振幅最初会向一个固定点下降,直到一个特定的时间点,之后振幅最终会发散。我们的分析包括分析和数值方法,并使用兰伯特 W 函数进行近似。推导出的近似解有效地捕捉到了不同延迟值下的生存动力学的定性方面。
We introduce a delay differential equation that manifests a distinctive
dynamical behavior. Specifically, the transient dynamics of this equation
demonstrate a unique ``reviving" amplitude phenomenon within certain ranges of
delay values. In this intriguing phenomenon, the amplitude initially decreases
towards a fixed point until a specific time point, after which it ultimately
diverges. Our analysis encompasses both analytical and numerical approaches,
incorporating an approximation using the Lambert W function. The derived
approximate solution effectively captures the qualitative aspects of the
reviving dynamics across various delay values.