Efficient synchronization of one-dimensional chaotic quadratic maps by different couling terms
Autor(a) principal: | |
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Data de Publicação: | 2010 |
Outros Autores: | , |
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. |
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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 |
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1799134826961305600 |