Modeling and analysis of random and stochastic input flows in the chemostat model

In this paper we study a new way to model noisy input flows in the chemostat model, based on the Ornstein-Uhlenbeck process. We introduce a parameter β as drift in the Langevin equation, that allows to bridge a gap between a pure Wiener process, which is a common way to model random disturbances, an...

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Autores: Caraballo Garrido, Tomás, Garrido Atienza, María José, López de la Cruz, Javier
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2019
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/92694
Acceso en línea:https://hdl.handle.net/11441/92694
https://doi.org/10.3934/dcdsb.2018280
Access Level:acceso abierto
Palabra clave:Chemostat model
Ornstein-Uhlenbeck process
Random dynamical system
Random attractor
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spelling Modeling and analysis of random and stochastic input flows in the chemostat modelCaraballo Garrido, TomásGarrido Atienza, María JoséLópez de la Cruz, JavierChemostat modelOrnstein-Uhlenbeck processRandom dynamical systemRandom attractorIn this paper we study a new way to model noisy input flows in the chemostat model, based on the Ornstein-Uhlenbeck process. We introduce a parameter β as drift in the Langevin equation, that allows to bridge a gap between a pure Wiener process, which is a common way to model random disturbances, and no noise at all. The value of the parameter β is related to the amplitude of the deviations observed on the realizations. We show that this modeling approach is well suited to represent noise on an input variable that has to take non-negative values for almost any time.European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)Ministerio de Economía y Competitividad (MINECO). EspañaJunta de AndalucíaAmerican Institute of Mathematical SciencesEcuaciones Diferenciales y Análisis NuméricoFQM314: Análisis Estocástico de Sistemas Diferenciales2019info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/92694https://doi.org/10.3934/dcdsb.2018280reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésDiscrete and Continuous Dynamical Systems - Series B, 24 (8), 3591-3614.MTM2015-63723-PP12-FQM-1492https://www.aimsciences.org/article/doi/10.3934/dcdsb.2018280info:eu-repo/semantics/openAccessoai:idus.us.es:11441/926942026-06-17T12:51:07Z
dc.title.none.fl_str_mv Modeling and analysis of random and stochastic input flows in the chemostat model
title Modeling and analysis of random and stochastic input flows in the chemostat model
spellingShingle Modeling and analysis of random and stochastic input flows in the chemostat model
Caraballo Garrido, Tomás
Chemostat model
Ornstein-Uhlenbeck process
Random dynamical system
Random attractor
title_short Modeling and analysis of random and stochastic input flows in the chemostat model
title_full Modeling and analysis of random and stochastic input flows in the chemostat model
title_fullStr Modeling and analysis of random and stochastic input flows in the chemostat model
title_full_unstemmed Modeling and analysis of random and stochastic input flows in the chemostat model
title_sort Modeling and analysis of random and stochastic input flows in the chemostat model
dc.creator.none.fl_str_mv Caraballo Garrido, Tomás
Garrido Atienza, María José
López de la Cruz, Javier
author Caraballo Garrido, Tomás
author_facet Caraballo Garrido, Tomás
Garrido Atienza, María José
López de la Cruz, Javier
author_role author
author2 Garrido Atienza, María José
López de la Cruz, Javier
author2_role author
author
dc.contributor.none.fl_str_mv Ecuaciones Diferenciales y Análisis Numérico
FQM314: Análisis Estocástico de Sistemas Diferenciales
dc.subject.none.fl_str_mv Chemostat model
Ornstein-Uhlenbeck process
Random dynamical system
Random attractor
topic Chemostat model
Ornstein-Uhlenbeck process
Random dynamical system
Random attractor
description In this paper we study a new way to model noisy input flows in the chemostat model, based on the Ornstein-Uhlenbeck process. We introduce a parameter β as drift in the Langevin equation, that allows to bridge a gap between a pure Wiener process, which is a common way to model random disturbances, and no noise at all. The value of the parameter β is related to the amplitude of the deviations observed on the realizations. We show that this modeling approach is well suited to represent noise on an input variable that has to take non-negative values for almost any time.
publishDate 2019
dc.date.none.fl_str_mv 2019
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/92694
https://doi.org/10.3934/dcdsb.2018280
url https://hdl.handle.net/11441/92694
https://doi.org/10.3934/dcdsb.2018280
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Discrete and Continuous Dynamical Systems - Series B, 24 (8), 3591-3614.
MTM2015-63723-P
P12-FQM-1492
https://www.aimsciences.org/article/doi/10.3934/dcdsb.2018280
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
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:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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