Control of chaotic transients: Yorke's Game of Survival

5 pages, 4 figures.-- PACS nr.: 05.45.Gg, 05.45.Pq.-- PMID: 14995689 [PubMed].

Detalles Bibliográficos
Autores: Aguirre, Jacobo, D'Ovidio, Francesco, Sanjuán, Miguel
Tipo de recurso: artículo
Fecha de publicación:2004
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/7503
Acceso en línea:http://hdl.handle.net/10261/7503
Access Level:acceso abierto
Palabra clave:[PACS] Control of chaos, applications of chaos
[PACS] Numerical simulations of chaotic systems
[PACS] Nonlinear dynamics and nonlinear dynamical systems
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spelling Control of chaotic transients: Yorke's Game of SurvivalAguirre, JacoboD'Ovidio, FrancescoSanjuán, Miguel[PACS] Control of chaos, applications of chaos[PACS] Numerical simulations of chaotic systems[PACS] Nonlinear dynamics and nonlinear dynamical systems5 pages, 4 figures.-- PACS nr.: 05.45.Gg, 05.45.Pq.-- PMID: 14995689 [PubMed].We consider the tent map as the prototype of a chaotic system with escapes. We show analytically that a small, bounded, but carefully chosen perturbation added to the system can trap forever an orbit close to the chaotic saddle, even in presence of noise of larger, although bounded, amplitude. This problem is focused as a two-person, mathematical game between two players called "the protagonist" and "the adversary." The protagonist's goal is to survive. He can lose but cannot win; the best he can do is survive to play another round, struggling ad infinitum. In the absence of actions by either player, the dynamics diverge, leaving a relatively safe region, and we say the protagonist loses. What makes survival difficult is that the adversary is allowed stronger "actions" than the protagonist. What makes survival possible is (i) the background dynamics (the tent map here) are chaotic and (ii) the protagonist knows the action of the adversary in choosing his response and is permitted to choose the initial point x(0) of the game. We use the "slope 3" tent map in an example of this problem. We show that it is possible for the protagonist to survive.J.A. and M.S.J. acknowledge financial support from the Spanish Ministry of Science and Technology under project BFM2000-0967, and from the Universidad Rey Juan Carlos under projects URJC-PGRAL-2001/02 and URJC-PIGE-02-04. F.d'O. acknowledges financial support from MCyT (Spain) and FEDER, project REN2001-0802-C02-01/MAR (IMAGEN).Peer reviewedAmerican Physical Society200820082004info:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_65012373 bytes118299 bytes74789 bytestext/plainapplication/pdfapplication/pdfhttp://hdl.handle.net/10261/7503reponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)Ingléshttp://dx.doi.org/10.1103/PhysRevE.69.016203info:eu-repo/semantics/openAccessoai:digital.csic.es:10261/75032026-05-22T06:33:51Z
dc.title.none.fl_str_mv Control of chaotic transients: Yorke's Game of Survival
title Control of chaotic transients: Yorke's Game of Survival
spellingShingle Control of chaotic transients: Yorke's Game of Survival
Aguirre, Jacobo
[PACS] Control of chaos, applications of chaos
[PACS] Numerical simulations of chaotic systems
[PACS] Nonlinear dynamics and nonlinear dynamical systems
title_short Control of chaotic transients: Yorke's Game of Survival
title_full Control of chaotic transients: Yorke's Game of Survival
title_fullStr Control of chaotic transients: Yorke's Game of Survival
title_full_unstemmed Control of chaotic transients: Yorke's Game of Survival
title_sort Control of chaotic transients: Yorke's Game of Survival
dc.creator.none.fl_str_mv Aguirre, Jacobo
D'Ovidio, Francesco
Sanjuán, Miguel
author Aguirre, Jacobo
author_facet Aguirre, Jacobo
D'Ovidio, Francesco
Sanjuán, Miguel
author_role author
author2 D'Ovidio, Francesco
Sanjuán, Miguel
author2_role author
author
dc.subject.none.fl_str_mv [PACS] Control of chaos, applications of chaos
[PACS] Numerical simulations of chaotic systems
[PACS] Nonlinear dynamics and nonlinear dynamical systems
topic [PACS] Control of chaos, applications of chaos
[PACS] Numerical simulations of chaotic systems
[PACS] Nonlinear dynamics and nonlinear dynamical systems
description 5 pages, 4 figures.-- PACS nr.: 05.45.Gg, 05.45.Pq.-- PMID: 14995689 [PubMed].
publishDate 2004
dc.date.none.fl_str_mv 2004
2008
2008
dc.type.none.fl_str_mv info:eu-repo/semantics/article
http://purl.org/coar/resource_type/c_6501
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dc.identifier.none.fl_str_mv http://hdl.handle.net/10261/7503
url http://hdl.handle.net/10261/7503
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv http://dx.doi.org/10.1103/PhysRevE.69.016203
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 2373 bytes
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dc.publisher.none.fl_str_mv American Physical Society
publisher.none.fl_str_mv American Physical Society
dc.source.none.fl_str_mv reponame:DIGITAL.CSIC. Repositorio Institucional del CSIC
instname:Consejo Superior de Investigaciones Científicas (CSIC)
instname_str Consejo Superior de Investigaciones Científicas (CSIC)
reponame_str DIGITAL.CSIC. Repositorio Institucional del CSIC
collection DIGITAL.CSIC. Repositorio Institucional del CSIC
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