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

Song, Keying; Ma, Wanbiao; Guo, Shuaiqi; Yan, Hai

doi:10.1186/s13662-018-1473-6

Cited by 10 publications

(3 citation statements)

References 42 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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“…Collection and extraction of microorganisms can be achieved by putting some suitable flocculants (e.g., aluminium salt or polyacrylamide) in the chemostat [6]. Flocculants can be used to precipitate microorganisms and then can also be used to precipitate pathogenic microorganisms in waste water (see [33]). Flocculation method has become very effective method in the chemostat and been widely used due to lower cost in the world.…”

mentioning

confidence: 99%

An analysis approach to permanence of a delay differential equations model of microorganism flocculation

Guo¹,

Cui²,

Ma³

2022

DCDS-B

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<p style='text-indent:20px;'>In this paper, we develop a delay differential equations model of microorganism flocculation with general monotonic functional responses, and then study the permanence of this model, which can ensure the sustainability of the collection of microorganisms. For a general differential system, the existence of a positive equilibrium can be obtained with the help of the persistence theory, whereas we give the existence conditions of a positive equilibrium by using the implicit function theorem. Then to obtain an explicit formula for the ultimate lower bound of microorganism concentration, we propose a general analysis method, which is different from the traditional approaches in persistence theory and also extends the analysis techniques of existing related works.</p>

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“…Otherwise, the varying environmental effects can not be neglected [5]. Many researchers have constructed stochastic models to describe the effects of the environmental noises on the dynamics of population [4,17,18,29,30,35,39,40,41,42,43,44,46,47]. For example, Imhof and Walcher [13] proposed a single microbe species stochastic chemostat model and showed the white noise may make the microorganism extinct.…”

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Asymptotic properties of a stochastic chemostat model with two distributed delays and nonlinear perturbation

Yu¹,

Yuan²

2020

Discrete &Amp; Continuous Dynamical Systems - B

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In this paper, a stochastic chemostat model with two distributed delays and nonlinear perturbation is proposed. We first transform the stochastic model into an equivalent high-dimensional system. Then we prove the existence and uniqueness of global positive solution of the model. Based on Khasminskii's theory, we study the existence of a stationary distribution of the model by constructing a suitable stochastic Lyapunov function. Then we also establish sufficient conditions for the extinction of the plankton. Finally, numerical simulations are carried out to illustrate the theoretical results and to conclude our study, which shows that environmental noise experienced by limiting nutrient completely determines the persistence and extinction of the plankton.2010 Mathematics Subject Classification. Primary: 34F05, 92B05, 37H10; Secondary: 60J70. 2373 2374 XINGWANG YU AND SANLING YUAN 2376 XINGWANG YU AND SANLING YUAN becomes the following form: dN = D(N 0 − N ) − aU (N )P + bγ t −∞ K 1 (t − s)P (s)ds dt + σ 1 N dB 1 (t), dP = P − (γ + D) + c t −∞

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

Cited by 10 publications

References 42 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

An analysis approach to permanence of a delay differential equations model of microorganism flocculation

Asymptotic properties of a stochastic chemostat model with two distributed delays and nonlinear perturbation

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