Partial control of chaos: How to avoid undesirable behaviors with small controls in presence of noise

This work was supported by the Spanish Ministry of Economy and Competitiveness under Project No. FIS2013-40653-P and by the Spanish State Research Agency (AEI) and the European Regional Development Fund (FEDER) under Project No. FIS2016-76883-P. MAFS acknowledges the jointly sponsored financial supp...

Descripción completa

Detalles Bibliográficos
Autores: Capeáns, Rubén, Sabuco, Juan, F.Sanjuán, Miguel A.
Tipo de recurso: artículo
Fecha de publicación:2018
País:España
Institución:Universidad Rey Juan Carlos
Repositorio:BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos
OAI Identifier:oai:burjcdigital.urjc.es:10115/31982
Acceso en línea:https://hdl.handle.net/10115/31982
Access Level:acceso abierto
Palabra clave:Transient chaos
delay-coordinate maps
time series
chaos control
hyperchaos.
id ES_bac0ca83cfe0c2e26516b236ecbc8469
oai_identifier_str oai:burjcdigital.urjc.es:10115/31982
network_acronym_str ES
network_name_str España
repository_id_str
spelling Partial control of chaos: How to avoid undesirable behaviors with small controls in presence of noiseCapeáns, RubénSabuco, JuanF.Sanjuán, Miguel A.Transient chaosdelay-coordinate mapstime serieschaos controlhyperchaos.This work was supported by the Spanish Ministry of Economy and Competitiveness under Project No. FIS2013-40653-P and by the Spanish State Research Agency (AEI) and the European Regional Development Fund (FEDER) under Project No. FIS2016-76883-P. MAFS acknowledges the jointly sponsored financial support by the Fulbright Program and the Spanish Ministry of Education (Program No. FMECD-ST-2016).The presence of a nonattractive chaotic set, also called chaotic saddle, in phase space implies the appearance of a finite time kind of chaos that is known as transient chaos. For a given dynamical system in a certain region of phase space with transient chaos, trajectories eventually abandon the chaotic region escaping to an external attractor, if no external intervention is done on the system. In some situations, this attractor may involve an undesirable behavior, so the application of a control in the system is necessary to avoid it. Both, the nonattractive nature of transient chaos and eventually the presence of noise may hinder this task. Recently, a new method to control chaos called partial control has been developed. The method is based on the existence of a set, called the safe set, that allows to sustain transient chaos by only using a small amount of control. The surprising result is that the trajectories can be controlled by using an amount of control smaller than the amount of noise affecting it. We present here a broad survey of results of this control method applied to a wide variety of dynamical systems. We also review here all the variations of the partial control method that have been developed so far. In all the cases various systems of different dimensionality are treated in order to see the potential of this method. We believe that this method is a step forward in controlling chaos in presence of disturbances.American Institute of Mathematical Sciences202420242018info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/10115/31982reponame:BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlosinstname:Universidad Rey Juan CarlosInglésinfo:eu-repo/semantics/openAccessoai:burjcdigital.urjc.es:10115/319822026-06-24T12:48:17Z
dc.title.none.fl_str_mv Partial control of chaos: How to avoid undesirable behaviors with small controls in presence of noise
title Partial control of chaos: How to avoid undesirable behaviors with small controls in presence of noise
spellingShingle Partial control of chaos: How to avoid undesirable behaviors with small controls in presence of noise
Capeáns, Rubén
Transient chaos
delay-coordinate maps
time series
chaos control
hyperchaos.
title_short Partial control of chaos: How to avoid undesirable behaviors with small controls in presence of noise
title_full Partial control of chaos: How to avoid undesirable behaviors with small controls in presence of noise
title_fullStr Partial control of chaos: How to avoid undesirable behaviors with small controls in presence of noise
title_full_unstemmed Partial control of chaos: How to avoid undesirable behaviors with small controls in presence of noise
title_sort Partial control of chaos: How to avoid undesirable behaviors with small controls in presence of noise
dc.creator.none.fl_str_mv Capeáns, Rubén
Sabuco, Juan
F.Sanjuán, Miguel A.
author Capeáns, Rubén
author_facet Capeáns, Rubén
Sabuco, Juan
F.Sanjuán, Miguel A.
author_role author
author2 Sabuco, Juan
F.Sanjuán, Miguel A.
author2_role author
author
dc.subject.none.fl_str_mv Transient chaos
delay-coordinate maps
time series
chaos control
hyperchaos.
topic Transient chaos
delay-coordinate maps
time series
chaos control
hyperchaos.
description This work was supported by the Spanish Ministry of Economy and Competitiveness under Project No. FIS2013-40653-P and by the Spanish State Research Agency (AEI) and the European Regional Development Fund (FEDER) under Project No. FIS2016-76883-P. MAFS acknowledges the jointly sponsored financial support by the Fulbright Program and the Spanish Ministry of Education (Program No. FMECD-ST-2016).
publishDate 2018
dc.date.none.fl_str_mv 2018
2024
2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/10115/31982
url https://hdl.handle.net/10115/31982
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.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 American Institute of Mathematical Sciences
publisher.none.fl_str_mv American Institute of Mathematical Sciences
dc.source.none.fl_str_mv reponame:BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos
instname:Universidad Rey Juan Carlos
instname_str Universidad Rey Juan Carlos
reponame_str BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos
collection BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869417945234407424
score 15.81155

Similares en LA Referencia