{"title":"Dynamics of large oscillator populations with random interactions","authors":"Arkady Pikovsky, Lev A. Smirnov","doi":"arxiv-2404.06193","DOIUrl":null,"url":null,"abstract":"We explore large populations of phase oscillators interacting via random\ncoupling functions. Two types of coupling terms, the Kuramoto-Daido coupling\nand the Winfree coupling, are considered. Under the assumption of statistical\nindependence of the phases and the couplings, we derive reduced averaged\nequations with effective non-random coupling terms. As a particular example, we\nstudy interactions that have the same shape but possess random coupling\nstrengths and random phase shifts. While randomness in coupling strengths just\nrenormalizes the interaction, a distribution of the phase shifts in coupling\nreshapes the coupling function.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"81 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-04-09","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-2404.06193","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
We explore large populations of phase oscillators interacting via random
coupling functions. Two types of coupling terms, the Kuramoto-Daido coupling
and the Winfree coupling, are considered. Under the assumption of statistical
independence of the phases and the couplings, we derive reduced averaged
equations with effective non-random coupling terms. As a particular example, we
study interactions that have the same shape but possess random coupling
strengths and random phase shifts. While randomness in coupling strengths just
renormalizes the interaction, a distribution of the phase shifts in coupling
reshapes the coupling function.