Efficient synchronization of one-dimensional chaotic quadratic maps by different couling terms

Detalhes bibliográficos
Autor(a) principal: Laureano, M.
Data de Publicação: 2010
Outros Autores: Mendes, D. A., Ferreira, M. A. M.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: https://ciencia.iscte-iul.pt/id/ci-pub-8886
http://hdl.handle.net/10071/13981
Resumo: The possibility of chaotic systems oscillate in a coherent and synchronized way is not an obvious phenomenon, since it is not possible to reproduce exactly the initial conditions and the sensitive dependence on initial conditions is one of the main characteristics associated with the chaotic behavior. We consider synchronization phenomena of discrete chaotic dynamical systems (identical or non-identical) with nonlinear unidirectional and bidirectional coupling schemes. In order to illustrate the synchronization methods present in this paper, we always use a system of two coupled chaotic quadratic maps. First, we present a systematic way to design unidirectional and bidirectional coupling schemes for synchronizing arbitrary pairs of one-dimensional chaotic maps. In dissipative coupling, we use two methods to study the stability of synchronous state: the linear stability and the Lyapunov functional analysis. Second, we explore other coupling schemes. With the unidirectional coupling based on the singular value decomposition it is possible to suppress the exponential divergence of the dynamics of the synchronization error and to guarantee linear stability of the synchronized state in all points of the state space. The other coupling scheme is asymmetric and appears in natural a family of analytic complex quadratic maps.
id RCAP_8d53df38600a8bd28b2269fa4969c0fd
oai_identifier_str oai:repositorio.iscte-iul.pt:10071/13981
network_acronym_str RCAP
network_name_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository_id_str 7160
spelling Efficient synchronization of one-dimensional chaotic quadratic maps by different couling termsEfficient synchronizationOne-dimensional chaotic quadratic mapsDifferent coupling termsThe possibility of chaotic systems oscillate in a coherent and synchronized way is not an obvious phenomenon, since it is not possible to reproduce exactly the initial conditions and the sensitive dependence on initial conditions is one of the main characteristics associated with the chaotic behavior. We consider synchronization phenomena of discrete chaotic dynamical systems (identical or non-identical) with nonlinear unidirectional and bidirectional coupling schemes. In order to illustrate the synchronization methods present in this paper, we always use a system of two coupled chaotic quadratic maps. First, we present a systematic way to design unidirectional and bidirectional coupling schemes for synchronizing arbitrary pairs of one-dimensional chaotic maps. In dissipative coupling, we use two methods to study the stability of synchronous state: the linear stability and the Lyapunov functional analysis. Second, we explore other coupling schemes. With the unidirectional coupling based on the singular value decomposition it is possible to suppress the exponential divergence of the dynamics of the synchronization error and to guarantee linear stability of the synchronized state in all points of the state space. The other coupling scheme is asymmetric and appears in natural a family of analytic complex quadratic maps.Progress IPS LLC2017-07-13T08:25:37Z2010-01-01T00:00:00Z20102017-07-13T08:24:57Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://ciencia.iscte-iul.pt/id/ci-pub-8886http://hdl.handle.net/10071/13981eng2078-0257Laureano, M.Mendes, D. A.Ferreira, M. A. M.info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-11-09T17:52:53Zoai:repositorio.iscte-iul.pt:10071/13981Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:26:25.132506Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Efficient synchronization of one-dimensional chaotic quadratic maps by different couling terms
title Efficient synchronization of one-dimensional chaotic quadratic maps by different couling terms
spellingShingle Efficient synchronization of one-dimensional chaotic quadratic maps by different couling terms
Laureano, M.
Efficient synchronization
One-dimensional chaotic quadratic maps
Different coupling terms
title_short Efficient synchronization of one-dimensional chaotic quadratic maps by different couling terms
title_full Efficient synchronization of one-dimensional chaotic quadratic maps by different couling terms
title_fullStr Efficient synchronization of one-dimensional chaotic quadratic maps by different couling terms
title_full_unstemmed Efficient synchronization of one-dimensional chaotic quadratic maps by different couling terms
title_sort Efficient synchronization of one-dimensional chaotic quadratic maps by different couling terms
author Laureano, M.
author_facet Laureano, M.
Mendes, D. A.
Ferreira, M. A. M.
author_role author
author2 Mendes, D. A.
Ferreira, M. A. M.
author2_role author
author
dc.contributor.author.fl_str_mv Laureano, M.
Mendes, D. A.
Ferreira, M. A. M.
dc.subject.por.fl_str_mv Efficient synchronization
One-dimensional chaotic quadratic maps
Different coupling terms
topic Efficient synchronization
One-dimensional chaotic quadratic maps
Different coupling terms
description The possibility of chaotic systems oscillate in a coherent and synchronized way is not an obvious phenomenon, since it is not possible to reproduce exactly the initial conditions and the sensitive dependence on initial conditions is one of the main characteristics associated with the chaotic behavior. We consider synchronization phenomena of discrete chaotic dynamical systems (identical or non-identical) with nonlinear unidirectional and bidirectional coupling schemes. In order to illustrate the synchronization methods present in this paper, we always use a system of two coupled chaotic quadratic maps. First, we present a systematic way to design unidirectional and bidirectional coupling schemes for synchronizing arbitrary pairs of one-dimensional chaotic maps. In dissipative coupling, we use two methods to study the stability of synchronous state: the linear stability and the Lyapunov functional analysis. Second, we explore other coupling schemes. With the unidirectional coupling based on the singular value decomposition it is possible to suppress the exponential divergence of the dynamics of the synchronization error and to guarantee linear stability of the synchronized state in all points of the state space. The other coupling scheme is asymmetric and appears in natural a family of analytic complex quadratic maps.
publishDate 2010
dc.date.none.fl_str_mv 2010-01-01T00:00:00Z
2010
2017-07-13T08:25:37Z
2017-07-13T08:24:57Z
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 https://ciencia.iscte-iul.pt/id/ci-pub-8886
http://hdl.handle.net/10071/13981
url https://ciencia.iscte-iul.pt/id/ci-pub-8886
http://hdl.handle.net/10071/13981
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 2078-0257
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Progress IPS LLC
publisher.none.fl_str_mv Progress IPS LLC
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
repository.mail.fl_str_mv
_version_ 1799134826961305600