Bifurcation analysis of a bioreactor model with variable yield coefficient and oxygen coefficient

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.

Download Full-text

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

ANZIAM Journal ◽

10.21914/anziamj.v53i0.5093 ◽

2012 ◽

Vol 53 ◽

pp. 155 ◽

Cited By ~ 4

Author(s):

Rubayyi Turki Alqahtani ◽

Mark I Nelson ◽

Annette L Worthy

Keyword(s):

Yield Coefficient ◽

Chemostat Model ◽

Variable Yield

Download Full-text

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

Complexity ◽

10.1155/2020/5065172 ◽

2020 ◽

Vol 2020 ◽

pp. 1-18 ◽

Cited By ~ 1

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.

Download Full-text

ON THE EXISTENCE OF CHAOTIC BEHAVIOUR IN PURE AND SIMPLE MICROBIAL COMPETITION: THE ROLE OF CONTOIS KINETICS

The ANZIAM Journal ◽

10.1017/s1446181113000345 ◽

2013 ◽

Vol 55 (2) ◽

pp. 162-174

Author(s):

MOHAMMAD ASIF ◽

EMAD ALI ◽

ABDELHAMID AJBAR

Keyword(s):

Period Doubling ◽

Chaotic Behaviour ◽

Yield Coefficient ◽

Competing Species ◽

Microbial Competition ◽

Complex Behaviour ◽

Variable Yield ◽

Proposed Model ◽

Limiting Nutrient ◽

Time Invariant

AbstractMicrobial competition for nutrients is a common phenomenon that occurs between species inhabiting the same environment. Bioreactors are often used for the study of microbial competition since the number and type of microbial species can be controlled, and the system can be isolated from other interactions that may occur between the competing species. A common type of competition is the so-called “pure and simple” competition, where the microbial populations interact in no other way except the competition for a single rate-limiting nutrient that affects their growth rates. The issue of whether pure and simple competition under time-invariant conditions can give rise to chaotic behaviour has been unresolved for decades. The third author recently showed, for the first time, that chaos can theoretically occur in these systems by analysing the dynamics of a model where both competing species grow following the biomass-dependent Contois model while the yield coefficients associated with the two species are substrate-dependent. In this paper we show that chaotic behaviour can occur in a much simpler model of pure and simple competition. We examine the case where only one species grows following the Contois model with variable yield coefficient while the other species is allowed to grow following the simple Monod model with constant yield. We show that while the static behaviour of the proposed model is quite simple, the dynamic behaviour is complex and involves period doubling culminating in chaos. The proposed model could serve as a basis to re-examine the importance of Contois kinetics in predicting complex behaviour in microbial competition.

Download Full-text