Study of the chemostat model with non-monotonic growth under random disturbances on the removal rate

We revisit the chemostat model with Haldane growth function, here subject to bounded random disturbances on the input flow rate, as often met in biotechnological or waste-water industry. We prove existence and uniqueness of global positive solution of the random dynamics and existence of absorbing a...

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Autores: Caraballo Garrido, Tomás, Colucci, Renato, López de la Cruz, Javier, Rapaport, Alain
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2020
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/104387
Acceso en línea:https://hdl.handle.net/11441/104387
https://doi.org/10.3934/mbe.2020382
Access Level:acceso abierto
Palabra clave:chemostat model
non-monotonic growth
bounded noise
Ornstein-Uhlenbeck
absorbing set
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spelling Study of the chemostat model with non-monotonic growth under random disturbances on the removal rateCaraballo Garrido, TomásColucci, RenatoLópez de la Cruz, JavierRapaport, Alainchemostat modelnon-monotonic growthbounded noiseOrnstein-Uhlenbeckabsorbing setWe revisit the chemostat model with Haldane growth function, here subject to bounded random disturbances on the input flow rate, as often met in biotechnological or waste-water industry. We prove existence and uniqueness of global positive solution of the random dynamics and existence of absorbing and attracting sets that are independent of the realizations of the noise. We study the long-time behavior of the random dynamics in terms of attracting sets, and provide first conditions under which biomass extinction cannot be avoided. We prove conditions for weak and strong persistence of the microbial species and provide lower bounds for the biomass concentration, as a relevant information for practitioners. The theoretical results are illustrated with numerical simulations.AIMS PressEcuaciones Diferenciales y Análisis Numérico2020info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/104387https://doi.org/10.3934/mbe.2020382reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésMathematical Biosciences and Engineering, 17 (6), 7480-1-7501-22.https://doi.org/10.3934/mbe.2020382info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1043872026-06-17T12:51:07Z
dc.title.none.fl_str_mv Study of the chemostat model with non-monotonic growth under random disturbances on the removal rate
title Study of the chemostat model with non-monotonic growth under random disturbances on the removal rate
spellingShingle Study of the chemostat model with non-monotonic growth under random disturbances on the removal rate
Caraballo Garrido, Tomás
chemostat model
non-monotonic growth
bounded noise
Ornstein-Uhlenbeck
absorbing set
title_short Study of the chemostat model with non-monotonic growth under random disturbances on the removal rate
title_full Study of the chemostat model with non-monotonic growth under random disturbances on the removal rate
title_fullStr Study of the chemostat model with non-monotonic growth under random disturbances on the removal rate
title_full_unstemmed Study of the chemostat model with non-monotonic growth under random disturbances on the removal rate
title_sort Study of the chemostat model with non-monotonic growth under random disturbances on the removal rate
dc.creator.none.fl_str_mv Caraballo Garrido, Tomás
Colucci, Renato
López de la Cruz, Javier
Rapaport, Alain
author Caraballo Garrido, Tomás
author_facet Caraballo Garrido, Tomás
Colucci, Renato
López de la Cruz, Javier
Rapaport, Alain
author_role author
author2 Colucci, Renato
López de la Cruz, Javier
Rapaport, Alain
author2_role author
author
author
dc.contributor.none.fl_str_mv Ecuaciones Diferenciales y Análisis Numérico
dc.subject.none.fl_str_mv chemostat model
non-monotonic growth
bounded noise
Ornstein-Uhlenbeck
absorbing set
topic chemostat model
non-monotonic growth
bounded noise
Ornstein-Uhlenbeck
absorbing set
description We revisit the chemostat model with Haldane growth function, here subject to bounded random disturbances on the input flow rate, as often met in biotechnological or waste-water industry. We prove existence and uniqueness of global positive solution of the random dynamics and existence of absorbing and attracting sets that are independent of the realizations of the noise. We study the long-time behavior of the random dynamics in terms of attracting sets, and provide first conditions under which biomass extinction cannot be avoided. We prove conditions for weak and strong persistence of the microbial species and provide lower bounds for the biomass concentration, as a relevant information for practitioners. The theoretical results are illustrated with numerical simulations.
publishDate 2020
dc.date.none.fl_str_mv 2020
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/104387
https://doi.org/10.3934/mbe.2020382
url https://hdl.handle.net/11441/104387
https://doi.org/10.3934/mbe.2020382
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Mathematical Biosciences and Engineering, 17 (6), 7480-1-7501-22.
https://doi.org/10.3934/mbe.2020382
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 AIMS Press
publisher.none.fl_str_mv AIMS Press
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 15,301603

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