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

Water ◽  
2021 ◽  
Vol 13 (22) ◽  
pp. 3266
Author(s):  
Milen Borisov ◽  
Neli Dimitrova ◽  
Plamena Zlateva
Keyword(s):  
Growth Rate ◽  
Time Delay ◽  
Mutual Influence ◽  
Equilibrium Points ◽  
Real Life ◽  
Biomass Growth ◽  
Stirred Bioreactor ◽  
Biological Time ◽  
Local Asymptotic Stability ◽  
Discrete Time Delay

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.

scholarly journals Global Stability Analysis of a Bioreactor Model for Phenol and Cresol Mixture Degradation

Processes ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 124
Author(s):  
Neli Dimitrova ◽  
Plamena Zlateva
Keyword(s):  
Specific Growth ◽  
Equilibrium Points ◽  
Nonlinear Ordinary Differential Equations ◽  
The Novel ◽  
Model Design ◽  
Stirred Bioreactor ◽  
Global Stability Analysis ◽  
Local Asymptotic Stability ◽  
Model Dynamics ◽  
Stability And Bifurcations

We propose a mathematical model for phenol and p-cresol mixture degradation in a continuously stirred bioreactor. The model is described by three nonlinear ordinary differential equations. The novel idea in the model design is the biomass specific growth rate, known as sum kinetics with interaction parameters (SKIP) and involving inhibition effects. We determine the equilibrium points of the model and study their local asymptotic stability and bifurcations with respect to a practically important parameter. Existence and uniqueness of positive solutions are proved. Global stabilizability of the model dynamics towards equilibrium points is established. The dynamic behavior of the solutions is demonstrated on some numerical examples.

scholarly journals Mathematical analysis of a cancer model with time-delay in tumor-immune interaction and stimulation processes

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Kaushik Dehingia ◽  
Hemanta Kumar Sarmah ◽  
Yamen Alharbi ◽  
Kamyar Hosseini
Keyword(s):  
Time Delay ◽  
Immune Responses ◽  
Periodic Solutions ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Cancer Model ◽  
Delay Effect ◽  
Discrete Time Delay ◽  
The Stability ◽  
Vital Parameters

AbstractIn this study, we discuss a cancer model considering discrete time-delay in tumor-immune interaction and stimulation processes. This study aims to analyze and observe the dynamics of the model along with variation of vital parameters and the delay effect on anti-tumor immune responses. We obtain sufficient conditions for the existence of equilibrium points and their stability. Existence of Hopf bifurcation at co-axial equilibrium is investigated. The stability of bifurcating periodic solutions is discussed, and the time length for which the solutions preserve the stability is estimated. Furthermore, we have derived the conditions for the direction of bifurcating periodic solutions. Theoretically, it was observed that the system undergoes different states if we vary the system’s parameters. Some numerical simulations are presented to verify the obtained mathematical results.

scholarly journals Effect of time delay on a detritus-based ecosystem

2006 ◽  
Vol 2006 ◽  
pp. 1-28 ◽  
Author(s):  
Nurul Huda Gazi ◽  
Malay Bandyopadhyay
Keyword(s):  
Time Delay ◽  
Equilibrium Points ◽  
Equation Model ◽  
Model System ◽  
Trophic Levels ◽  
Dynamical Analysis ◽  
Discrete Time Delay ◽  
Growth Equations ◽  
The Stability ◽  
Delay Differential

Models of detritus-based ecosystems with delay have received a great deal of attention for the last few decades. This paper deals with the dynamical analysis of a nonlinear model of a detritus-based ecosystem involving detritivores and predator of detritivores. We have obtained the criteria for local stability of various equilibrium points and persistence of the model system. Next, we have introduced discrete time delay due to recycling of dead organic matters and gestation of nutrients to the growth equations of various trophic levels. With delay differential equation model system we have studied the effect of time delay on the stability behaviour. Next, we have obtained an estimate for the length of time delay to preserve the stability of the model system. Finally, the existence of Hopf-bifurcating small amplitude periodic solutions is derived by considering time delay as a bifurcation parameter.

A competition model with herd behaviour and allee effect

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2529-2542
Author(s):  
Prosenjit Sen ◽  
Alakes Maiti ◽  
G.P. Samanta
Keyword(s):  
Time Delay ◽  
Numerical Simulations ◽  
Discrete Time ◽  
Local Stability ◽  
Allee Effect ◽  
Equilibrium Points ◽  
Uniform Boundedness ◽  
Competition Model ◽  
Discrete Time Delay ◽  
Herd Behaviour

In this work we have studied the deterministic behaviours of a competition model with herd behaviour and Allee effect. The uniform boundedness of the system has been studied. Criteria for local stability at equilibrium points are derived. The effect of discrete time-delay on the model is investigated. We have carried out numerical simulations to validate the analytical findings. The biological implications of our analytical and numerical findings are discussed.

Discrete-Time Delay Dynamics of Boundedly Rational Monopoly

2012 ◽  
Author(s):  
Akio Matsumato ◽  
Ferenc Szidarovsky
Keyword(s):  
Time Delay ◽  
Discrete Time ◽  
Discrete Time Delay

scholarly journals Precise regulation of the relative rates of surface area and volume synthesis in bacterial cells growing in dynamic environments

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Handuo Shi ◽  
Yan Hu ◽  
Pascal D. Odermatt ◽  
Carlos G. Gonzalez ◽  
Lichao Zhang ◽  
...  
Keyword(s):  
Growth Rate ◽  
Time Delay ◽  
Surface Area ◽  
Environmental Changes ◽  
Volume Ratio ◽  
Dynamic Environments ◽  
Bacterial Cells ◽  
Bacterial Growth Rate ◽  
State Size ◽  
Insight Into

AbstractThe steady-state size of bacterial cells correlates with nutrient-determined growth rate. Here, we explore how rod-shaped bacterial cells regulate their morphology during rapid environmental changes. We quantify cellular dimensions throughout passage cycles of stationary-phase cells diluted into fresh medium and grown back to saturation. We find that cells exhibit characteristic dynamics in surface area to volume ratio (SA/V), which are conserved across genetic and chemical perturbations as well as across species and growth temperatures. A mathematical model with a single fitting parameter (the time delay between surface and volume synthesis) is quantitatively consistent with our SA/V experimental observations. The model supports that this time delay is due to differential expression of volume and surface-related genes, and that the first division after dilution occurs at a tightly controlled SA/V. Our minimal model thus provides insight into the connections between bacterial growth rate and cell shape in dynamic environments.

Stability analysis of a general family of nonlinear positive discrete time-delay systems

2016 ◽  
Vol 89 (7) ◽  
pp. 1303-1315 ◽  
Author(s):  
P. T. Nam ◽  
V. N. Phat ◽  
P. N. Pathirana ◽  
H. Trinh
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Discrete Time ◽  
Delay Systems ◽  
Time Delay Systems ◽  
General Family ◽  
Discrete Time Delay
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