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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| Format: | Article |
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MDPI AG
2021-11-01
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| Series: | Water |
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| Online Access: | https://www.mdpi.com/2073-4441/13/22/3266 |
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| author | Milen Borisov Neli Dimitrova Plamena Zlateva |
| author_facet | Milen Borisov Neli Dimitrova Plamena Zlateva |
| author_sort | Milen Borisov |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-03-10T04:58:27Z |
| format | Article |
| id | doaj.art-b181d1745c1c431e81dcd2a4a7adb13c |
| institution | Directory Open Access Journal |
| issn | 2073-4441 |
| language | English |
| last_indexed | 2024-03-10T04:58:27Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Water |
| spelling | doaj.art-b181d1745c1c431e81dcd2a4a7adb13c2023-11-23T02:01:11ZengMDPI AGWater2073-44412021-11-011322326610.3390/w13223266Time-Delayed Bioreactor Model of Phenol and Cresol Mixture Degradation with Interaction KineticsMilen Borisov0Neli Dimitrova1Plamena Zlateva2Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Block 8, 1113 Sofia, BulgariaInstitute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Block 8, 1113 Sofia, BulgariaInstitute of Robotics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Block 2, 1113 Sofia, BulgariaThis 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.https://www.mdpi.com/2073-4441/13/22/3266wastewaterphenol and <i>p</i>-cresol mixture biodegradationbioreactor modelSKIP kineticsdiscrete delayequilibrium points |
| spellingShingle | Milen Borisov Neli Dimitrova Plamena Zlateva Time-Delayed Bioreactor Model of Phenol and Cresol Mixture Degradation with Interaction Kinetics Water wastewater phenol and <i>p</i>-cresol mixture biodegradation bioreactor model SKIP kinetics discrete delay equilibrium points |
| title | 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_short | 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 |
| topic | wastewater phenol and <i>p</i>-cresol mixture biodegradation bioreactor model SKIP kinetics discrete delay equilibrium points |
| url | https://www.mdpi.com/2073-4441/13/22/3266 |
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