Correlation times in stochastic equations with delayed feedback and multiplicative noise

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Autor(es): dc.contributorMcGill University-
Autor(es): dc.contributorUniversidade Estadual Paulista (UNESP)-
Autor(es): dc.creatorGaudreault, Mathieu-
Autor(es): dc.creatorBerbert, Juliana Militão-
Autor(es): dc.creatorViñals, Jorge-
Data de aceite: dc.date.accessioned2025-08-21T23:12:00Z-
Data de disponibilização: dc.date.available2025-08-21T23:12:00Z-
Data de envio: dc.date.issued2022-04-28-
Data de envio: dc.date.issued2022-04-28-
Data de envio: dc.date.issued2011-01-11-
Fonte completa do material: dc.identifierhttp://dx.doi.org/10.1103/PhysRevE.83.011903-
Fonte completa do material: dc.identifierhttp://hdl.handle.net/11449/226211-
Fonte: dc.identifier.urihttp://educapes.capes.gov.br/handle/11449/226211-
Descrição: dc.descriptionWe 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.-
Descrição: dc.descriptionDepartment of Physics McGill University, Montreal, QC H3A 2T8-
Descrição: dc.descriptionInstituto de Física Teórica (IFT) Universidade Estadual Paulista (UNESP), Caixa Postal 70532-2, 01156-970 São Paulo, São Paulo-
Descrição: dc.descriptionInstituto de Física Teórica (IFT) Universidade Estadual Paulista (UNESP), Caixa Postal 70532-2, 01156-970 São Paulo, São Paulo-
Idioma: dc.languageen-
Relação: dc.relationPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics-
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Título: dc.titleCorrelation times in stochastic equations with delayed feedback and multiplicative noise-
Tipo de arquivo: dc.typelivro digital-
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