Time-Delayed Bioreactor Model of Phenol and Cresol Mixture Degradation with Interaction Kinetics

This paper is devoted to a mathematical model for phenol and <i>p</i>-cresol mixture degradation in a continuously stirred bioreactor. The biomass specific growth rate is presented as sum kinetics with interaction parameters (SKIP). A discrete time delay is introduced and incorporated in...

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Autores principales:	Milen Borisov, Neli Dimitrova, Plamena Zlateva
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	wastewater phenol and <i>p</i>-cresol mixture biodegradation bioreactor model SKIP kinetics discrete delay equilibrium points Hydraulic engineering TC1-978 Water supply for domestic and industrial purposes TD201-500
Acceso en línea:	https://doaj.org/article/b181d1745c1c431e81dcd2a4a7adb13c
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spelling	oai:doaj.org-article:b181d1745c1c431e81dcd2a4a7adb13c2021-11-25T19:16:10ZTime-Delayed Bioreactor Model of Phenol and Cresol Mixture Degradation with Interaction Kinetics10.3390/w132232662073-4441https://doaj.org/article/b181d1745c1c431e81dcd2a4a7adb13c2021-11-01T00:00:00Zhttps://www.mdpi.com/2073-4441/13/22/3266https://doaj.org/toc/2073-4441This paper is devoted to a mathematical model for phenol and <i>p</i>-cresol mixture degradation in a continuously stirred bioreactor. The biomass specific growth rate is presented as sum kinetics with interaction parameters (SKIP). A discrete time delay is introduced and incorporated into the biomass growth response. These two aspects—the mutual influence of the two substrates and the natural biological time delay in the biomass growth rate—are new in the scientific literature concerning bioreactor (chemostat) models. The equilibrium points of the model are determined and their local asymptotic stability as well as the occurrence of local Hopf bifurcations are studied in dependence on the delay parameter. The existence and uniqueness of positive solutions are established, and the global stabilizability of the model dynamics is proved for certain values of the delay. Numerical simulations illustrate the global behavior of the model solutions as well as the transient oscillations as a result of the Hopf bifurcation. The performed theoretical analysis and computer simulations can be successfully used to better understand the biodegradation dynamics of the chemical compounds in the bioreactor and to predict and control the system behavior in real life conditions.Milen BorisovNeli DimitrovaPlamena ZlatevaMDPI AGarticlewastewaterphenol and <i>p</i>-cresol mixture biodegradationbioreactor modelSKIP kineticsdiscrete delayequilibrium pointsHydraulic engineeringTC1-978Water supply for domestic and industrial purposesTD201-500ENWater, Vol 13, Iss 3266, p 3266 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	wastewater phenol and <i>p</i>-cresol mixture biodegradation bioreactor model SKIP kinetics discrete delay equilibrium points Hydraulic engineering TC1-978 Water supply for domestic and industrial purposes TD201-500
spellingShingle	wastewater phenol and <i>p</i>-cresol mixture biodegradation bioreactor model SKIP kinetics discrete delay equilibrium points Hydraulic engineering TC1-978 Water supply for domestic and industrial purposes TD201-500 Milen Borisov Neli Dimitrova Plamena Zlateva Time-Delayed Bioreactor Model of Phenol and Cresol Mixture Degradation with Interaction Kinetics
description	This paper is devoted to a mathematical model for phenol and <i>p</i>-cresol mixture degradation in a continuously stirred bioreactor. The biomass specific growth rate is presented as sum kinetics with interaction parameters (SKIP). A discrete time delay is introduced and incorporated into the biomass growth response. These two aspects—the mutual influence of the two substrates and the natural biological time delay in the biomass growth rate—are new in the scientific literature concerning bioreactor (chemostat) models. The equilibrium points of the model are determined and their local asymptotic stability as well as the occurrence of local Hopf bifurcations are studied in dependence on the delay parameter. The existence and uniqueness of positive solutions are established, and the global stabilizability of the model dynamics is proved for certain values of the delay. Numerical simulations illustrate the global behavior of the model solutions as well as the transient oscillations as a result of the Hopf bifurcation. The performed theoretical analysis and computer simulations can be successfully used to better understand the biodegradation dynamics of the chemical compounds in the bioreactor and to predict and control the system behavior in real life conditions.
format	article
author	Milen Borisov Neli Dimitrova Plamena Zlateva
author_facet	Milen Borisov Neli Dimitrova Plamena Zlateva
author_sort	Milen Borisov
title	Time-Delayed Bioreactor Model of Phenol and Cresol Mixture Degradation with Interaction Kinetics
title_short	Time-Delayed Bioreactor Model of Phenol and Cresol Mixture Degradation with Interaction Kinetics
title_full	Time-Delayed Bioreactor Model of Phenol and Cresol Mixture Degradation with Interaction Kinetics
title_fullStr	Time-Delayed Bioreactor Model of Phenol and Cresol Mixture Degradation with Interaction Kinetics
title_full_unstemmed	Time-Delayed Bioreactor Model of Phenol and Cresol Mixture Degradation with Interaction Kinetics
title_sort	time-delayed bioreactor model of phenol and cresol mixture degradation with interaction kinetics
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/b181d1745c1c431e81dcd2a4a7adb13c
work_keys_str_mv	AT milenborisov timedelayedbioreactormodelofphenolandcresolmixturedegradationwithinteractionkinetics AT nelidimitrova timedelayedbioreactormodelofphenolandcresolmixturedegradationwithinteractionkinetics AT plamenazlateva timedelayedbioreactormodelofphenolandcresolmixturedegradationwithinteractionkinetics
_version_	1718410116034723840

Time-Delayed Bioreactor Model of Phenol and Cresol Mixture Degradation with Interaction Kinetics

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