scholarly journals Analysis of a Chemostat Model with Variable Yield Coefficient and Substrate Inhibition: Contois Growth Kinetics

2014 ◽  
Vol 202 (3) ◽  
pp. 332-344 ◽  
Author(s):  
Rubayyi T. Alqahtani ◽  
Mark I. Nelson ◽  
Annette L. Worthy
Keyword(s):  
Growth Kinetics ◽  
Substrate Inhibition ◽  
Yield Coefficient ◽  
Chemostat Model ◽  
Variable Yield

Non-existence of periodic solutions in a model of continuous fermentation

1992 ◽  
Vol 438 (1903) ◽  
pp. 311-318 ◽  
Keyword(s):  
Periodic Solutions ◽  
Continuous Fermentation ◽  
Substrate Inhibition ◽  
Decay Rates ◽  
Yield Coefficient ◽  
General Criterion ◽  
Variable Yield ◽  
Uptake Rates ◽  
Existence Of Periodic Solutions ◽  
Micro Organisms

A general criterion is given for the absence of non-trivial periodic solutions in a model of continuous fermentation. In the model there is one species of micro-organism and one single limiting substrate. The model allows for uptake rates with substrate inhibition, variable yield coefficients, variable endogenous decay rates, separation of micro-organisms from the outflowing stream, and non-zero micro-organism feed rates. The criterion implies in particular the absence of non-trivial periodic solutions if the yield coefficient and the endogenous decay rate are constant.

scholarly journals Analysis of a chemostat model with variable yield coefficient: Contois kinetics

2012 ◽  
Vol 53 ◽  
pp. 155 ◽  
Author(s):  
Rubayyi Turki Alqahtani ◽  
Mark I Nelson ◽  
Annette L Worthy
Keyword(s):  
Yield Coefficient ◽  
Chemostat Model ◽  
Variable Yield

scholarly journals Stochastic Characteristics and Optimal Control for a Stochastic Chemostat Model with Variable Yield

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-18 ◽  
Author(s):  
Rong Yan ◽  
Shulin Sun
Keyword(s):  
Stochastic Model ◽  
Hamiltonian Function ◽  
Growth Function ◽  
Necessary Condition ◽  
Yield Coefficient ◽  
Chemostat Model ◽  
Variable Yield ◽  
Persistence In The Mean ◽  
Limiting Nutrient ◽  
Stochastic Characteristics

In this paper, a stochastic chemostat model with variable yield and Contois growth function is investigated. The yield coefficient depends on the limiting nutrient, and the environmental noises are given by independent standard Brownian motions. First, the existence and uniqueness of global positive solution are proved. Second, by using stochastic Lyapunov function, Itô’s formula, and some important inequalities, stochastic characteristics for the stochastic model are studied, including the extinction of micro-organism, the strong persistence in the mean of micro-organism and, the existence of a unique stationary distribution of the stochastic model. Third, the necessary condition of an optimal stochastic control for the stochastic model is established by Hamiltonian function. In addition, some numerical simulations are carried out to illustrate the theoretical results and the influence of the variable yield on the microorganism.

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