Modelling and optimal control for an impulsive dynamical system in microbial fed-batch culture

Gao, Jinggui; Shen, Banyu; Feng, Enmin; Xiu, Zhilong

doi:10.1007/s40314-013-0012-z

Cited by 25 publications

(13 citation statements)

References 16 publications

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“…Due to the fact that the interaction of the populations in the ecosystem is very complex and lacks strict control, it is not possible to directly investigate the interrelationships among the various groups. The chemostat is a laboratory apparatus used for the continuous culture of microorganism, and it plays an important role in exploring the growth of microorganism in a deterministic environment [1][2][3][4][5][6][7][8][9]. By controlling the input and output rate of the chemostat, we can investigate the interaction between microorganisms and the dynamic behavior of microbial growth in nutrition conditions.…”

Section: Introductionmentioning

confidence: 99%

Dynamical analysis of multi-nutrient and single microorganism chemostat model in a polluted environment

Chi

Zhao

2018

Adv Differ Equ

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In this paper, we propose a multi-nutrient and single microorganism chemostat model with stochastic effect and impulsive toxicant input. Firstly, for the system neglecting stochastic effect, we investigate the global dynamics including the existence and global asymptotic stability of 'microorganism-extinction' periodic solution, as well as the permanence of the system. Then, for the stochastic differential system with impulsive effect, we discuss the persistence and extinction of microorganisms with stochastic effect in a polluted environment. Our results indicate that the stochastic disturbance can lead to microbial extinction. Moreover, the concentration of toxicant will also affect the survival of microorganisms. Finally, numerical simulations are carried out to illustrate our theoretical results. MSC: 60H10; 65C30; 91B70

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Section: Introductionmentioning

confidence: 99%

Dynamical analysis of multi-nutrient and single microorganism chemostat model in a polluted environment

Chi

Zhao

2018

Adv Differ Equ

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“…The chemostat can be used to model nutrient consumption and microbial competition [20][21][22][23][24][25][26][27]. In some cases, microorganisms can produce toxins or inhibitors against its competitors.…”

Section: Introduction and Statement Of Model Formulationmentioning

confidence: 99%

A class of dynamic models describing microbial flocculant with nutrient competition and metabolic products in wastewater treatment

Song

Guo

et al. 2018

Adv Differ Equ

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In this paper, based on the related theories of microbial continuous culture, fermentation dynamics, and microbial flocculant, a class of dynamic models which describe microbial flocculant with resource competition and metabolic products in wastewater treatment is proposed. By analyzing the global dynamic properties of the model, the feasibility of employing microbial metabolites as flocculant to remove harmful microorganisms is considered. MSC: 92B05; 34D20

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“…Chemostat is commonly used to describe the dynamics of a microbial population in a continuous bioreactor in which microorganisms grow on a substrate and has attracted great interest of many scholars [1][2][3][4][5][6][7][8], since it was first introduced by Monod [9]. A single simple species chemostat model with Michaelis-Menten-Monod functional response was proposed by [9] as follows:…”

Section: Introductionmentioning

confidence: 99%

Threshold Dynamics of a Stochastic Chemostat Model with Two Nutrients and One Microorganism

Zhang

Miao

Zhang

2017

Mathematical Problems in Engineering

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A new stochastic chemostat model with two substitutable nutrients and one microorganism is proposed and investigated. Firstly, for the corresponding deterministic model, the threshold for extinction and permanence of the microorganism is obtained by analyzing the stability of the equilibria. Then, for the stochastic model, the threshold of the stochastic chemostat for extinction and permanence of the microorganism is explored. Difference of the threshold of the deterministic model and the stochastic model shows that a large stochastic disturbance can affect the persistence of the microorganism and is harmful to the cultivation of the microorganism. To illustrate this phenomenon, we give some computer simulations with different intensity of stochastic noise disturbance.

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Modelling and optimal control for an impulsive dynamical system in microbial fed-batch culture

Cited by 25 publications

References 16 publications

Dynamical analysis of multi-nutrient and single microorganism chemostat model in a polluted environment

Dynamical analysis of multi-nutrient and single microorganism chemostat model in a polluted environment

A class of dynamic models describing microbial flocculant with nutrient competition and metabolic products in wastewater treatment

Threshold Dynamics of a Stochastic Chemostat Model with Two Nutrients and One Microorganism

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