How to embed shrimps in parameter planes of the Lorenz system

Bibliographic Details
Main Author: Rech P.C.*
Publication Date: 2017
Format: Article
Language: eng
Source: Repositório Institucional da Udesc
dARK ID: ark:/33523/00130000049hr
Download full: https://repositorio.udesc.br/handle/UDESC/7071
Summary: © 2017 The Royal Swedish Academy of Sciences.Shrimps are typical periodic islands present in chaotic regions of parameter planes of nonlinear dynamical systems. Such periodic structures have been observed in several different fields including mathematical models simulating lasers, electronic circuits, chemical reactions, neural networks, and biological systems. As far as I know the existence of shrimps in parameter planes of the Lorenz system has never been reported. This paper describes how to display such structures embedded in chaotic regions of parameter planes of the Lorenz system. This is accomplished by considering a shift in the x variable of the differential equation. Additionally it is shown that these periodic structures may appear organized in period-adding sequences.
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spelling How to embed shrimps in parameter planes of the Lorenz system© 2017 The Royal Swedish Academy of Sciences.Shrimps are typical periodic islands present in chaotic regions of parameter planes of nonlinear dynamical systems. Such periodic structures have been observed in several different fields including mathematical models simulating lasers, electronic circuits, chemical reactions, neural networks, and biological systems. As far as I know the existence of shrimps in parameter planes of the Lorenz system has never been reported. This paper describes how to display such structures embedded in chaotic regions of parameter planes of the Lorenz system. This is accomplished by considering a shift in the x variable of the differential equation. Additionally it is shown that these periodic structures may appear organized in period-adding sequences.2024-12-06T13:18:32Z2017info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article1402-489610.1088/1402-4896/aa5f61https://repositorio.udesc.br/handle/UDESC/7071ark:/33523/00130000049hrPhysica Scripta924Rech P.C.*engreponame:Repositório Institucional da Udescinstname:Universidade do Estado de Santa Catarina (UDESC)instacron:UDESCinfo:eu-repo/semantics/openAccess2024-12-07T20:53:01Zoai:repositorio.udesc.br:UDESC/7071Biblioteca Digital de Teses e Dissertaçõeshttps://pergamumweb.udesc.br/biblioteca/index.phpPRIhttps://repositorio-api.udesc.br/server/oai/requestri@udesc.bropendoar:63912024-12-07T20:53:01Repositório Institucional da Udesc - Universidade do Estado de Santa Catarina (UDESC)false
dc.title.none.fl_str_mv How to embed shrimps in parameter planes of the Lorenz system
title How to embed shrimps in parameter planes of the Lorenz system
spellingShingle How to embed shrimps in parameter planes of the Lorenz system
Rech P.C.*
title_short How to embed shrimps in parameter planes of the Lorenz system
title_full How to embed shrimps in parameter planes of the Lorenz system
title_fullStr How to embed shrimps in parameter planes of the Lorenz system
title_full_unstemmed How to embed shrimps in parameter planes of the Lorenz system
title_sort How to embed shrimps in parameter planes of the Lorenz system
author Rech P.C.*
author_facet Rech P.C.*
author_role author
dc.contributor.author.fl_str_mv Rech P.C.*
description © 2017 The Royal Swedish Academy of Sciences.Shrimps are typical periodic islands present in chaotic regions of parameter planes of nonlinear dynamical systems. Such periodic structures have been observed in several different fields including mathematical models simulating lasers, electronic circuits, chemical reactions, neural networks, and biological systems. As far as I know the existence of shrimps in parameter planes of the Lorenz system has never been reported. This paper describes how to display such structures embedded in chaotic regions of parameter planes of the Lorenz system. This is accomplished by considering a shift in the x variable of the differential equation. Additionally it is shown that these periodic structures may appear organized in period-adding sequences.
publishDate 2017
dc.date.none.fl_str_mv 2017
2024-12-06T13:18:32Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv 1402-4896
10.1088/1402-4896/aa5f61
https://repositorio.udesc.br/handle/UDESC/7071
dc.identifier.dark.fl_str_mv ark:/33523/00130000049hr
identifier_str_mv 1402-4896
10.1088/1402-4896/aa5f61
ark:/33523/00130000049hr
url https://repositorio.udesc.br/handle/UDESC/7071
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Physica Scripta
92
4
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.source.none.fl_str_mv reponame:Repositório Institucional da Udesc
instname:Universidade do Estado de Santa Catarina (UDESC)
instacron:UDESC
instname_str Universidade do Estado de Santa Catarina (UDESC)
instacron_str UDESC
institution UDESC
reponame_str Repositório Institucional da Udesc
collection Repositório Institucional da Udesc
repository.name.fl_str_mv Repositório Institucional da Udesc - Universidade do Estado de Santa Catarina (UDESC)
repository.mail.fl_str_mv ri@udesc.br
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