Correlation times in stochastic equations with delayed feedback and multiplicative noise
Autor(a) principal: | |
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Data de Publicação: | 2011 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1103/PhysRevE.83.011903 http://hdl.handle.net/11449/226211 |
Resumo: | We obtain the characteristic correlation time associated with a model stochastic differential equation that includes the normal form of a pitchfork bifurcation and delayed feedback. In particular, the validity of the common assumption of statistical independence between the state at time t and that at t-τ, where τ is the delay time, is examined. We find that the correlation time diverges at the model's bifurcation line, thus signaling a sharp bifurcation threshold, and the failure of statistical independence near threshold. We determine the correlation time both by numerical integration of the governing equation, and analytically in the limit of small τ. The correlation time T diverges as T~a⊃-1, where a is the control parameter so that a=0 is the bifurcation threshold. The small-τ expansion correctly predicts the location of the bifurcation threshold, but there are systematic deviations in the magnitude of the correlation time. © 2011 American Physical Society. |
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Repositório Institucional da UNESP |
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Correlation times in stochastic equations with delayed feedback and multiplicative noiseWe obtain the characteristic correlation time associated with a model stochastic differential equation that includes the normal form of a pitchfork bifurcation and delayed feedback. In particular, the validity of the common assumption of statistical independence between the state at time t and that at t-τ, where τ is the delay time, is examined. We find that the correlation time diverges at the model's bifurcation line, thus signaling a sharp bifurcation threshold, and the failure of statistical independence near threshold. We determine the correlation time both by numerical integration of the governing equation, and analytically in the limit of small τ. The correlation time T diverges as T~a⊃-1, where a is the control parameter so that a=0 is the bifurcation threshold. The small-τ expansion correctly predicts the location of the bifurcation threshold, but there are systematic deviations in the magnitude of the correlation time. © 2011 American Physical Society.Department of Physics McGill University, Montreal, QC H3A 2T8Instituto de Física Teórica (IFT) Universidade Estadual Paulista (UNESP), Caixa Postal 70532-2, 01156-970 São Paulo, São PauloInstituto de Física Teórica (IFT) Universidade Estadual Paulista (UNESP), Caixa Postal 70532-2, 01156-970 São Paulo, São PauloMcGill UniversityUniversidade Estadual Paulista (UNESP)Gaudreault, MathieuBerbert, Juliana Militão [UNESP]Viñals, Jorge2022-04-28T22:02:09Z2022-04-28T22:02:09Z2011-01-11info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1103/PhysRevE.83.011903Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, v. 83, n. 1, 2011.1539-37551550-2376http://hdl.handle.net/11449/22621110.1103/PhysRevE.83.0119032-s2.0-78751515887Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengPhysical Review E - Statistical, Nonlinear, and Soft Matter Physicsinfo:eu-repo/semantics/openAccess2022-04-28T22:02:09Zoai:repositorio.unesp.br:11449/226211Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T23:49:16.190634Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Correlation times in stochastic equations with delayed feedback and multiplicative noise |
title |
Correlation times in stochastic equations with delayed feedback and multiplicative noise |
spellingShingle |
Correlation times in stochastic equations with delayed feedback and multiplicative noise Gaudreault, Mathieu |
title_short |
Correlation times in stochastic equations with delayed feedback and multiplicative noise |
title_full |
Correlation times in stochastic equations with delayed feedback and multiplicative noise |
title_fullStr |
Correlation times in stochastic equations with delayed feedback and multiplicative noise |
title_full_unstemmed |
Correlation times in stochastic equations with delayed feedback and multiplicative noise |
title_sort |
Correlation times in stochastic equations with delayed feedback and multiplicative noise |
author |
Gaudreault, Mathieu |
author_facet |
Gaudreault, Mathieu Berbert, Juliana Militão [UNESP] Viñals, Jorge |
author_role |
author |
author2 |
Berbert, Juliana Militão [UNESP] Viñals, Jorge |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
McGill University Universidade Estadual Paulista (UNESP) |
dc.contributor.author.fl_str_mv |
Gaudreault, Mathieu Berbert, Juliana Militão [UNESP] Viñals, Jorge |
description |
We obtain the characteristic correlation time associated with a model stochastic differential equation that includes the normal form of a pitchfork bifurcation and delayed feedback. In particular, the validity of the common assumption of statistical independence between the state at time t and that at t-τ, where τ is the delay time, is examined. We find that the correlation time diverges at the model's bifurcation line, thus signaling a sharp bifurcation threshold, and the failure of statistical independence near threshold. We determine the correlation time both by numerical integration of the governing equation, and analytically in the limit of small τ. The correlation time T diverges as T~a⊃-1, where a is the control parameter so that a=0 is the bifurcation threshold. The small-τ expansion correctly predicts the location of the bifurcation threshold, but there are systematic deviations in the magnitude of the correlation time. © 2011 American Physical Society. |
publishDate |
2011 |
dc.date.none.fl_str_mv |
2011-01-11 2022-04-28T22:02:09Z 2022-04-28T22:02:09Z |
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 |
http://dx.doi.org/10.1103/PhysRevE.83.011903 Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, v. 83, n. 1, 2011. 1539-3755 1550-2376 http://hdl.handle.net/11449/226211 10.1103/PhysRevE.83.011903 2-s2.0-78751515887 |
url |
http://dx.doi.org/10.1103/PhysRevE.83.011903 http://hdl.handle.net/11449/226211 |
identifier_str_mv |
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, v. 83, n. 1, 2011. 1539-3755 1550-2376 10.1103/PhysRevE.83.011903 2-s2.0-78751515887 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1808129555364315136 |