由 Ornstein-Uhlenbeck 噪声驱动的系统中的多模态性。

IF 2.7 2区数学 Q1 MATHEMATICS, APPLIED

Chaos Pub Date : 2024-11-01 DOI:10.1063/5.0228666

Bartłomiej Dybiec

{"title":"由 Ornstein-Uhlenbeck 噪声驱动的系统中的多模态性。","authors":"Bartłomiej Dybiec","doi":"10.1063/5.0228666","DOIUrl":null,"url":null,"abstract":"The presence of noise in nonlinear dynamical systems can significantly change their properties. Here, we study the properties of a noise perturbed motion in a single-well potential of |x|n (n>0) type. We explore under what conditions the action of the Ornstein-Uhlenbeck noise induces bimodality of stationary states in static, single-well, power-law potentials. In particular, we inspect the transition from unimodality (n⩽2) to bimodality (n>2). Results of numerical simulations are compared with estimates obtained from the unified colored-noise approximation. Furthermore, we explore the role of a harmonic addition to the general single-well power-law potentials showing its constructive or destructive role.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"34 11","pages":""},"PeriodicalIF":2.7000,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Multimodality in systems driven by Ornstein-Uhlenbeck noise.\",\"authors\":\"Bartłomiej Dybiec\",\"doi\":\"10.1063/5.0228666\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The presence of noise in nonlinear dynamical systems can significantly change their properties. Here, we study the properties of a noise perturbed motion in a single-well potential of |x|n (n>0) type. We explore under what conditions the action of the Ornstein-Uhlenbeck noise induces bimodality of stationary states in static, single-well, power-law potentials. In particular, we inspect the transition from unimodality (n⩽2) to bimodality (n>2). Results of numerical simulations are compared with estimates obtained from the unified colored-noise approximation. Furthermore, we explore the role of a harmonic addition to the general single-well power-law potentials showing its constructive or destructive role.\",\"PeriodicalId\":9974,\"journal\":{\"name\":\"Chaos\",\"volume\":\"34 11\",\"pages\":\"\"},\"PeriodicalIF\":2.7000,\"publicationDate\":\"2024-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Chaos\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1063/5.0228666\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Chaos","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1063/5.0228666","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

非线性动力学系统中噪声的存在会显著改变其特性。在此，我们研究了 |x|n (n>0) 型单阱势中受噪声扰动的运动特性。我们探讨了在什么条件下，Ornstein-Uhlenbeck 噪声的作用会导致静态、单孔、幂律势中静止状态的双峰性。特别是，我们考察了从单峰性（n⩽2）到双峰性（n>2）的过渡。我们将数值模拟的结果与统一色噪近似的估计值进行了比较。此外，我们还探讨了一般单阱幂律势的谐波附加作用，显示了其建设性或破坏性作用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Multimodality in systems driven by Ornstein-Uhlenbeck noise.

The presence of noise in nonlinear dynamical systems can significantly change their properties. Here, we study the properties of a noise perturbed motion in a single-well potential of |x|n (n>0) type. We explore under what conditions the action of the Ornstein-Uhlenbeck noise induces bimodality of stationary states in static, single-well, power-law potentials. In particular, we inspect the transition from unimodality (n⩽2) to bimodality (n>2). Results of numerical simulations are compared with estimates obtained from the unified colored-noise approximation. Furthermore, we explore the role of a harmonic addition to the general single-well power-law potentials showing its constructive or destructive role.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Chaos 物理-物理：数学物理

CiteScore

5.20

自引率

13.80%

发文量

448

审稿时长

2.3 months

期刊介绍： Chaos: An Interdisciplinary Journal of Nonlinear Science is a peer-reviewed journal devoted to increasing the understanding of nonlinear phenomena and describing the manifestations in a manner comprehensible to researchers from a broad spectrum of disciplines.