{"title":"Chaotification and chaos control of q-homographic map.","authors":"Aishwaraya, V V M S Chandramouli","doi":"10.1063/5.0215334","DOIUrl":null,"url":null,"abstract":"<p><p>This paper concerns the dynamical study of the q-deformed homographic map, namely, the q-homographic map, where q-deformation is introduced by Jagannathan and Sinha with the inspiration from Tsalli's q-exponential function. We analyze the q-homographic map by computing its basic nonlinear dynamics, bifurcation analysis, and topological entropy. We use the notion of a false derivative and the generalized Lambert W function of the rational type to estimate the upper bound on the number of fixed points of the q-homographic map. Furthermore, we discuss chaotification of the q-deformed map to enhance its complexity, which consists of adding the remainder of multiple scaling of the map's value for the next generation using the multiple remainder operator. The chaotified q-homographic map shows high complexity and the presence of robust chaos, which have been theoretically and graphically analyzed using various dynamical techniques. Moreover, to control the period-doubling bifurcations and chaos in the q-homographic map, we use the feedback control technique. The theoretical discussion of chaos control is illustrated by numerical simulations.</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/10.1063/5.0215334","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
This paper concerns the dynamical study of the q-deformed homographic map, namely, the q-homographic map, where q-deformation is introduced by Jagannathan and Sinha with the inspiration from Tsalli's q-exponential function. We analyze the q-homographic map by computing its basic nonlinear dynamics, bifurcation analysis, and topological entropy. We use the notion of a false derivative and the generalized Lambert W function of the rational type to estimate the upper bound on the number of fixed points of the q-homographic map. Furthermore, we discuss chaotification of the q-deformed map to enhance its complexity, which consists of adding the remainder of multiple scaling of the map's value for the next generation using the multiple remainder operator. The chaotified q-homographic map shows high complexity and the presence of robust chaos, which have been theoretically and graphically analyzed using various dynamical techniques. Moreover, to control the period-doubling bifurcations and chaos in the q-homographic map, we use the feedback control technique. The theoretical discussion of chaos control is illustrated by numerical simulations.
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.