1. Time-Delayed Bioreactor Model of Phenol and Cresol Mixture Degradation with Interaction Kinetics
- Author
-
Neli Dimitrova, Plamena Zlateva, and Milen Borisov
- Subjects
Hopf Bifurcations ,Geography, Planning and Development ,Chemostat ,Aquatic Science ,Wastewater ,stability analysis ,Biochemistry ,Equilibrium Points ,symbols.namesake ,phenol and p-cresol mixture biodegradation ,Exponential stability ,SKIP kinetics ,Bioreactor ,Uniqueness ,Numerical Simulation ,wastewater ,TD201-500 ,Water Science and Technology ,Mathematics ,Hopf bifurcation ,Equilibrium point ,bioreactor model ,Computer simulation ,Water supply for domestic and industrial purposes ,Bioreactor Model ,Hydraulic engineering ,Hopf bifurcations ,discrete delay ,SKIP Kinetics ,Stability Analysis ,Discrete time and continuous time ,numerical simulation ,equilibrium points ,symbols ,Phenol and P-cresol Mixture Biodegradation ,Discrete Delay ,Biological system ,TC1-978 - Abstract
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.
- Published
- 2021