On the dynamics of two-dimensional dissipative discontinuous maps
Autor(a) principal: | |
---|---|
Data de Publicação: | 2020 |
Outros Autores: | , , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1016/j.chaos.2019.109520 http://hdl.handle.net/11449/198223 |
Resumo: | Some dynamical properties for a dissipative two-dimensional discontinuous standard mapping are considered. The mapping, in action-angle variables, is parameterized by two control parameters; namely, k ≥ 0 controlling the intensity of the nonlinearity and γ ∈ [0, 1] representing the dissipation. The case of γ=0 recovers the non-dissipative model while any γ ≠ 0 yields to the breaking of area preservation; hence leading to the existence of attractors, including chaotic ones. We show that when starting from a large initial action, the dynamics converges to chaotic attractors through an exponential decay in time, while the speed of the decay depends on the dissipation intensity. We also investigate the positive Lyapunov exponents and describe their behavior as a function of the control parameters. |
id |
UNSP_e6dcf7246dbb76f3a75043a109ad961d |
---|---|
oai_identifier_str |
oai:repositorio.unesp.br:11449/198223 |
network_acronym_str |
UNSP |
network_name_str |
Repositório Institucional da UNESP |
repository_id_str |
2946 |
spelling |
On the dynamics of two-dimensional dissipative discontinuous mapsChaotic attractorsDissipative discontinuous standard mappingLyapunov exponentsSome dynamical properties for a dissipative two-dimensional discontinuous standard mapping are considered. The mapping, in action-angle variables, is parameterized by two control parameters; namely, k ≥ 0 controlling the intensity of the nonlinearity and γ ∈ [0, 1] representing the dissipation. The case of γ=0 recovers the non-dissipative model while any γ ≠ 0 yields to the breaking of area preservation; hence leading to the existence of attractors, including chaotic ones. We show that when starting from a large initial action, the dynamics converges to chaotic attractors through an exponential decay in time, while the speed of the decay depends on the dissipation intensity. We also investigate the positive Lyapunov exponents and describe their behavior as a function of the control parameters.Universidade Estadual PaulistaFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Universidade Estadual Paulista (UNESP) Campus de São João da Boa Vista, Av. Profa. Isette Corrêa Fontão, 505 – CEP:Universidade Estadual Paulista (UNESP) Departamento de Física Av.24A 1515, Bela Vista – CEP:Departamento de Matemática Aplicada e Estatística Instituto de Ciências Matemáticas e de Computação Universidade de São Paulo, Campus de São Carlos, Caixa Postal 668Instituto de Física Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48The Abdus Salam - ICTP, Strada Costiera, 11Universidade Estadual Paulista (UNESP) Campus de São João da Boa Vista, Av. Profa. Isette Corrêa Fontão, 505 – CEP:Universidade Estadual Paulista (UNESP) Departamento de Física Av.24A 1515, Bela Vista – CEP:FAPESP: 2014/18672-8FAPESP: 2017/14414-2FAPESP: 2018/14685-9FAPESP: 2019/06931-2CNPq: 303242/2018-3CNPq: 303707/2015-1CNPq: 311105/2015-7CNPq: 421254/2016-5Universidade Estadual Paulista (Unesp)Universidade de São Paulo (USP)Benemérita Universidad Autónoma de PueblaThe Abdus Salam - ICTPPerre, Rodrigo M. [UNESP]Carneiro, Bárbara P. [UNESP]Méndez-Bermúdez, J. A.Leonel, Edson D. [UNESP]de Oliveira, Juliano A. [UNESP]2020-12-12T01:06:53Z2020-12-12T01:06:53Z2020-02-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1016/j.chaos.2019.109520Chaos, Solitons and Fractals, v. 131.0960-0779http://hdl.handle.net/11449/19822310.1016/j.chaos.2019.1095202-s2.0-85075857449Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengChaos, Solitons and Fractalsinfo:eu-repo/semantics/openAccess2021-10-23T10:02:20Zoai:repositorio.unesp.br:11449/198223Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T17:17:00.693560Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
On the dynamics of two-dimensional dissipative discontinuous maps |
title |
On the dynamics of two-dimensional dissipative discontinuous maps |
spellingShingle |
On the dynamics of two-dimensional dissipative discontinuous maps Perre, Rodrigo M. [UNESP] Chaotic attractors Dissipative discontinuous standard mapping Lyapunov exponents |
title_short |
On the dynamics of two-dimensional dissipative discontinuous maps |
title_full |
On the dynamics of two-dimensional dissipative discontinuous maps |
title_fullStr |
On the dynamics of two-dimensional dissipative discontinuous maps |
title_full_unstemmed |
On the dynamics of two-dimensional dissipative discontinuous maps |
title_sort |
On the dynamics of two-dimensional dissipative discontinuous maps |
author |
Perre, Rodrigo M. [UNESP] |
author_facet |
Perre, Rodrigo M. [UNESP] Carneiro, Bárbara P. [UNESP] Méndez-Bermúdez, J. A. Leonel, Edson D. [UNESP] de Oliveira, Juliano A. [UNESP] |
author_role |
author |
author2 |
Carneiro, Bárbara P. [UNESP] Méndez-Bermúdez, J. A. Leonel, Edson D. [UNESP] de Oliveira, Juliano A. [UNESP] |
author2_role |
author author author author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) Universidade de São Paulo (USP) Benemérita Universidad Autónoma de Puebla The Abdus Salam - ICTP |
dc.contributor.author.fl_str_mv |
Perre, Rodrigo M. [UNESP] Carneiro, Bárbara P. [UNESP] Méndez-Bermúdez, J. A. Leonel, Edson D. [UNESP] de Oliveira, Juliano A. [UNESP] |
dc.subject.por.fl_str_mv |
Chaotic attractors Dissipative discontinuous standard mapping Lyapunov exponents |
topic |
Chaotic attractors Dissipative discontinuous standard mapping Lyapunov exponents |
description |
Some dynamical properties for a dissipative two-dimensional discontinuous standard mapping are considered. The mapping, in action-angle variables, is parameterized by two control parameters; namely, k ≥ 0 controlling the intensity of the nonlinearity and γ ∈ [0, 1] representing the dissipation. The case of γ=0 recovers the non-dissipative model while any γ ≠ 0 yields to the breaking of area preservation; hence leading to the existence of attractors, including chaotic ones. We show that when starting from a large initial action, the dynamics converges to chaotic attractors through an exponential decay in time, while the speed of the decay depends on the dissipation intensity. We also investigate the positive Lyapunov exponents and describe their behavior as a function of the control parameters. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020-12-12T01:06:53Z 2020-12-12T01:06:53Z 2020-02-01 |
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 |
http://dx.doi.org/10.1016/j.chaos.2019.109520 Chaos, Solitons and Fractals, v. 131. 0960-0779 http://hdl.handle.net/11449/198223 10.1016/j.chaos.2019.109520 2-s2.0-85075857449 |
url |
http://dx.doi.org/10.1016/j.chaos.2019.109520 http://hdl.handle.net/11449/198223 |
identifier_str_mv |
Chaos, Solitons and Fractals, v. 131. 0960-0779 10.1016/j.chaos.2019.109520 2-s2.0-85075857449 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Chaos, Solitons and Fractals |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1808128783143665664 |