L F B Souza, R Egydio de Carvalho, R L Viana, I L Caldas
{"title":"Shearless and periodic attractors in the dissipative Labyrinthic map.","authors":"L F B Souza, R Egydio de Carvalho, R L Viana, I L Caldas","doi":"10.1063/5.0225577","DOIUrl":null,"url":null,"abstract":"<p><p>The Labyrinthic map is a two-dimensional area-preserving map that features a robust transport barrier known as the shearless curve. In this study, we explore a dissipative version of this map, examining how dissipation affects the shearless curve and leads to the emergence of quasi-periodic or chaotic attractors, referred to as shearless attractors. We present a route to chaos of the shearless attractor known as the Curry-Yorke route. To investigate the multi-stability of the system, we employ basin entropy and boundary basin entropy analyses to characterize diverse scenarios. Additionally, we numerically investigate the dynamic periodic structures known as \"shrimps\" and \"Arnold tongues\" by varying the parameters of the system.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"34 12","pages":""},"PeriodicalIF":2.7000,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Chaos","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1063/5.0225577","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
Abstract
The Labyrinthic map is a two-dimensional area-preserving map that features a robust transport barrier known as the shearless curve. In this study, we explore a dissipative version of this map, examining how dissipation affects the shearless curve and leads to the emergence of quasi-periodic or chaotic attractors, referred to as shearless attractors. We present a route to chaos of the shearless attractor known as the Curry-Yorke route. To investigate the multi-stability of the system, we employ basin entropy and boundary basin entropy analyses to characterize diverse scenarios. Additionally, we numerically investigate the dynamic periodic structures known as "shrimps" and "Arnold tongues" by varying the parameters of the system.
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.