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Article

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

by 1,†, 1,*,† and 2
1
Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Block 8, 1113 Sofia, Bulgaria
2
Institute of Robotics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Block 2, 1113 Sofia, Bulgaria
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editors: Yongmei Li and Jacek Mąkinia
Water 2021, 13(22), 3266; https://doi.org/10.3390/w13223266
Received: 19 September 2021 / Revised: 12 November 2021 / Accepted: 15 November 2021 / Published: 17 November 2021
This paper is devoted to a mathematical model for phenol and p-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. View Full-Text
Keywords: wastewater; phenol and p-cresol mixture biodegradation; bioreactor model; SKIP kinetics; discrete delay; equilibrium points; stability analysis; Hopf bifurcations; numerical simulation wastewater; phenol and p-cresol mixture biodegradation; bioreactor model; SKIP kinetics; discrete delay; equilibrium points; stability analysis; Hopf bifurcations; numerical simulation
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MDPI and ACS Style

Borisov, M.; Dimitrova, N.; Zlateva, P. Time-Delayed Bioreactor Model of Phenol and Cresol Mixture Degradation with Interaction Kinetics. Water 2021, 13, 3266. https://doi.org/10.3390/w13223266

AMA Style

Borisov M, Dimitrova N, Zlateva P. Time-Delayed Bioreactor Model of Phenol and Cresol Mixture Degradation with Interaction Kinetics. Water. 2021; 13(22):3266. https://doi.org/10.3390/w13223266

Chicago/Turabian Style

Borisov, Milen, Neli Dimitrova, and Plamena Zlateva. 2021. "Time-Delayed Bioreactor Model of Phenol and Cresol Mixture Degradation with Interaction Kinetics" Water 13, no. 22: 3266. https://doi.org/10.3390/w13223266

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