Matheus Rolim Sales, Michele Mugnaine, Edson Denis Leonel, Iberê L Caldas, José D Szezech
{"title":"Shrinking shrimp-shaped domains and multistability in the dissipative asymmetric kicked rotor map.","authors":"Matheus Rolim Sales, Michele Mugnaine, Edson Denis Leonel, Iberê L Caldas, José D Szezech","doi":"10.1063/5.0233324","DOIUrl":null,"url":null,"abstract":"<p><p>An interesting feature in dissipative nonlinear systems is the emergence of characteristic domains in parameter space that exhibit periodic temporal evolution, known as shrimp-shaped domains. We investigate the parameter space of the dissipative asymmetric kicked rotor map and show that, in the regime of strong dissipation, the shrimp-shaped domains repeat themselves as the nonlinearity parameter increases while maintaining the same period. We analyze the dependence of the length of each periodic domain with the nonlinearity parameter, revealing that it follows a power law with the same exponent regardless of the dissipation parameter. Additionally, we find that the distance between adjacent shrimp-shaped domains is scaling invariant with respect to the dissipation parameter. Furthermore, we show that for weaker dissipation, a multistable scenario emerges within the periodic domains. We find that as the dissipation gets weaker, the ratio of multistable parameters for each periodic domain increases, and the area of the periodic basin decreases as the nonlinearity parameter increases.</p>","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/10.1063/5.0233324","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
An interesting feature in dissipative nonlinear systems is the emergence of characteristic domains in parameter space that exhibit periodic temporal evolution, known as shrimp-shaped domains. We investigate the parameter space of the dissipative asymmetric kicked rotor map and show that, in the regime of strong dissipation, the shrimp-shaped domains repeat themselves as the nonlinearity parameter increases while maintaining the same period. We analyze the dependence of the length of each periodic domain with the nonlinearity parameter, revealing that it follows a power law with the same exponent regardless of the dissipation parameter. Additionally, we find that the distance between adjacent shrimp-shaped domains is scaling invariant with respect to the dissipation parameter. Furthermore, we show that for weaker dissipation, a multistable scenario emerges within the periodic domains. We find that as the dissipation gets weaker, the ratio of multistable parameters for each periodic domain increases, and the area of the periodic basin decreases as the nonlinearity parameter increases.
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.