Low-dimensional phase-locked states in the zakharov equations
Autor(a) principal: | |
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Data de Publicação: | 1996 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFRGS |
Texto Completo: | http://hdl.handle.net/10183/103639 |
Resumo: | In this paper we identify phase-locked states among the solutions of the Zakharov equations. Locked states appear as resonant island chains in the appropriate Poincaré plots, with the relevant surface of section obtained by projecting out the full dynamical set on a subspace defined in terms of a pair of center-manifold variables. This pair allows an accurate canonical description of the system immediately after an inverse pitchfork bifurcation destabilizes an initial homogeneous steady state. If one is very close to the bifurcation point, nonlinear saturation of the initial instability is provided by quasistatic integrable ion-acoustic fluctuations, but as one proceeds away from that point, resonant nonintegrable ion-acoustic fluctuations become gradually more important; we show that the phase-locked states result from those resonant fluctuations. If one is not too far from the pitchfork bifurcation, locking is the stable asymptotic state of the interaction. As one moves farther away, locking exists only over long but finite amounts of time. In addition, the resonance separatrix appears to bring the first chaotic activity into the system. |
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Oliveira, Glaucius Iahnke deOliveira, Luiz Paulo Luna deRizzato, Felipe Barbedo2014-09-23T02:12:32Z19961063-651Xhttp://hdl.handle.net/10183/103639000179421In this paper we identify phase-locked states among the solutions of the Zakharov equations. Locked states appear as resonant island chains in the appropriate Poincaré plots, with the relevant surface of section obtained by projecting out the full dynamical set on a subspace defined in terms of a pair of center-manifold variables. This pair allows an accurate canonical description of the system immediately after an inverse pitchfork bifurcation destabilizes an initial homogeneous steady state. If one is very close to the bifurcation point, nonlinear saturation of the initial instability is provided by quasistatic integrable ion-acoustic fluctuations, but as one proceeds away from that point, resonant nonintegrable ion-acoustic fluctuations become gradually more important; we show that the phase-locked states result from those resonant fluctuations. If one is not too far from the pitchfork bifurcation, locking is the stable asymptotic state of the interaction. As one moves farther away, locking exists only over long but finite amounts of time. In addition, the resonance separatrix appears to bring the first chaotic activity into the system.application/pdfengPhysical Review. E, Statistical Physics, Plasmas, Fluids and Related Interdisciplinary Topics. New York. Vol. 54, no. 4 (Oct. 1996), p. 3239-3249Sistemas caóticosLow-dimensional phase-locked states in the zakharov equationsEstrangeiroinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFRGSinstname:Universidade Federal do Rio Grande do Sul (UFRGS)instacron:UFRGSORIGINAL000179421.pdf000179421.pdfTexto completo (inglês)application/pdf283648http://www.lume.ufrgs.br/bitstream/10183/103639/1/000179421.pdfc247b1f267e8cfaa2f49aa87859c6a69MD51TEXT000179421.pdf.txt000179421.pdf.txtExtracted Texttext/plain35140http://www.lume.ufrgs.br/bitstream/10183/103639/2/000179421.pdf.txt447bd2da4bd16e2dd3ec1c8ae14a0779MD52THUMBNAIL000179421.pdf.jpg000179421.pdf.jpgGenerated Thumbnailimage/jpeg2102http://www.lume.ufrgs.br/bitstream/10183/103639/3/000179421.pdf.jpged6df6e1759bfb29687041119c033766MD5310183/1036392023-09-02 03:35:26.779656oai:www.lume.ufrgs.br:10183/103639Repositório de PublicaçõesPUBhttps://lume.ufrgs.br/oai/requestopendoar:2023-09-02T06:35:26Repositório Institucional da UFRGS - Universidade Federal do Rio Grande do Sul (UFRGS)false |
dc.title.pt_BR.fl_str_mv |
Low-dimensional phase-locked states in the zakharov equations |
title |
Low-dimensional phase-locked states in the zakharov equations |
spellingShingle |
Low-dimensional phase-locked states in the zakharov equations Oliveira, Glaucius Iahnke de Sistemas caóticos |
title_short |
Low-dimensional phase-locked states in the zakharov equations |
title_full |
Low-dimensional phase-locked states in the zakharov equations |
title_fullStr |
Low-dimensional phase-locked states in the zakharov equations |
title_full_unstemmed |
Low-dimensional phase-locked states in the zakharov equations |
title_sort |
Low-dimensional phase-locked states in the zakharov equations |
author |
Oliveira, Glaucius Iahnke de |
author_facet |
Oliveira, Glaucius Iahnke de Oliveira, Luiz Paulo Luna de Rizzato, Felipe Barbedo |
author_role |
author |
author2 |
Oliveira, Luiz Paulo Luna de Rizzato, Felipe Barbedo |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Oliveira, Glaucius Iahnke de Oliveira, Luiz Paulo Luna de Rizzato, Felipe Barbedo |
dc.subject.por.fl_str_mv |
Sistemas caóticos |
topic |
Sistemas caóticos |
description |
In this paper we identify phase-locked states among the solutions of the Zakharov equations. Locked states appear as resonant island chains in the appropriate Poincaré plots, with the relevant surface of section obtained by projecting out the full dynamical set on a subspace defined in terms of a pair of center-manifold variables. This pair allows an accurate canonical description of the system immediately after an inverse pitchfork bifurcation destabilizes an initial homogeneous steady state. If one is very close to the bifurcation point, nonlinear saturation of the initial instability is provided by quasistatic integrable ion-acoustic fluctuations, but as one proceeds away from that point, resonant nonintegrable ion-acoustic fluctuations become gradually more important; we show that the phase-locked states result from those resonant fluctuations. If one is not too far from the pitchfork bifurcation, locking is the stable asymptotic state of the interaction. As one moves farther away, locking exists only over long but finite amounts of time. In addition, the resonance separatrix appears to bring the first chaotic activity into the system. |
publishDate |
1996 |
dc.date.issued.fl_str_mv |
1996 |
dc.date.accessioned.fl_str_mv |
2014-09-23T02:12:32Z |
dc.type.driver.fl_str_mv |
Estrangeiro info:eu-repo/semantics/article |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10183/103639 |
dc.identifier.issn.pt_BR.fl_str_mv |
1063-651X |
dc.identifier.nrb.pt_BR.fl_str_mv |
000179421 |
identifier_str_mv |
1063-651X 000179421 |
url |
http://hdl.handle.net/10183/103639 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.ispartof.pt_BR.fl_str_mv |
Physical Review. E, Statistical Physics, Plasmas, Fluids and Related Interdisciplinary Topics. New York. Vol. 54, no. 4 (Oct. 1996), p. 3239-3249 |
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openAccess |
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