Recovering parameters from self-similar structures in phase space of dissipative systems with constant Jacobian

Detalhes bibliográficos
Autor(a) principal: Rech P.C.*
Data de Publicação: 2000
Outros Autores: Beims M.W., Gallas J.A.C.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da Udesc
dARK ID: ark:/33523/001300000bj9f
Texto Completo: https://repositorio.udesc.br/handle/UDESC/10536
Resumo: We show that dissipative dynamical systems with constant Jacobian allow one to recover numerical values of control parameters under which the system is operating. This is done by performing measurements on self-similar (fractal) structures in phase space. We illustrate parameter recovery explicitly for the Ikeda laser ring-cavity map and the Henon map. The first model involves transcendental equations of motion and can be solved only numerically. Analytical results are obtained for the Henon map. In both cases, the dissipation rate is recovered from the speed at which fractal `fingers' making up basins of attraction accumulate towards basin boundaries.
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spelling Recovering parameters from self-similar structures in phase space of dissipative systems with constant JacobianWe show that dissipative dynamical systems with constant Jacobian allow one to recover numerical values of control parameters under which the system is operating. This is done by performing measurements on self-similar (fractal) structures in phase space. We illustrate parameter recovery explicitly for the Ikeda laser ring-cavity map and the Henon map. The first model involves transcendental equations of motion and can be solved only numerically. Analytical results are obtained for the Henon map. In both cases, the dissipation rate is recovered from the speed at which fractal `fingers' making up basins of attraction accumulate towards basin boundaries.2024-12-06T19:54:27Z2000info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlep. 273 - 2760378-437110.1016/S0378-4371(00)00166-7https://repositorio.udesc.br/handle/UDESC/10536ark:/33523/001300000bj9fPhysica A: Statistical Mechanics and its Applications2831Rech P.C.*Beims M.W.Gallas J.A.C.engreponame:Repositório Institucional da Udescinstname:Universidade do Estado de Santa Catarina (UDESC)instacron:UDESCinfo:eu-repo/semantics/openAccess2024-12-07T21:09:31Zoai:repositorio.udesc.br:UDESC/10536Biblioteca Digital de Teses e Dissertaçõeshttps://pergamumweb.udesc.br/biblioteca/index.phpPRIhttps://repositorio-api.udesc.br/server/oai/requestri@udesc.bropendoar:63912024-12-07T21:09:31Repositório Institucional da Udesc - Universidade do Estado de Santa Catarina (UDESC)false
dc.title.none.fl_str_mv Recovering parameters from self-similar structures in phase space of dissipative systems with constant Jacobian
title Recovering parameters from self-similar structures in phase space of dissipative systems with constant Jacobian
spellingShingle Recovering parameters from self-similar structures in phase space of dissipative systems with constant Jacobian
Rech P.C.*
title_short Recovering parameters from self-similar structures in phase space of dissipative systems with constant Jacobian
title_full Recovering parameters from self-similar structures in phase space of dissipative systems with constant Jacobian
title_fullStr Recovering parameters from self-similar structures in phase space of dissipative systems with constant Jacobian
title_full_unstemmed Recovering parameters from self-similar structures in phase space of dissipative systems with constant Jacobian
title_sort Recovering parameters from self-similar structures in phase space of dissipative systems with constant Jacobian
author Rech P.C.*
author_facet Rech P.C.*
Beims M.W.
Gallas J.A.C.
author_role author
author2 Beims M.W.
Gallas J.A.C.
author2_role author
author
dc.contributor.author.fl_str_mv Rech P.C.*
Beims M.W.
Gallas J.A.C.
description We show that dissipative dynamical systems with constant Jacobian allow one to recover numerical values of control parameters under which the system is operating. This is done by performing measurements on self-similar (fractal) structures in phase space. We illustrate parameter recovery explicitly for the Ikeda laser ring-cavity map and the Henon map. The first model involves transcendental equations of motion and can be solved only numerically. Analytical results are obtained for the Henon map. In both cases, the dissipation rate is recovered from the speed at which fractal `fingers' making up basins of attraction accumulate towards basin boundaries.
publishDate 2000
dc.date.none.fl_str_mv 2000
2024-12-06T19:54:27Z
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 0378-4371
10.1016/S0378-4371(00)00166-7
https://repositorio.udesc.br/handle/UDESC/10536
dc.identifier.dark.fl_str_mv ark:/33523/001300000bj9f
identifier_str_mv 0378-4371
10.1016/S0378-4371(00)00166-7
ark:/33523/001300000bj9f
url https://repositorio.udesc.br/handle/UDESC/10536
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Physica A: Statistical Mechanics and its Applications
283
1
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv p. 273 - 276
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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