Periodic solution of a chemostat model with variable yield and impulsive state feedback control

Li, Zuxiong; Chen, Lansun; Liu, Zhijun

doi:10.1016/j.apm.2011.07.069

Cited by 50 publications

(14 citation statements)

References 28 publications

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“…The chemostat model is mainly used for laboratory theoretical research. So far, many scholars have obtained significant results for chemostat models [1][2][3][4][5][6][7][8][9][10][11]. While the populations in nature suffer from instantaneous discontinuous interference (for example, toxic input, seasonal harvest, and spraying pesticides), this interference phenomenon can be described as an impulse mathematically [12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of an Impulsive Stochastic Nonautonomous Chemostat Model with Two Different Growth Rates in a Polluted Environment

Meng

2019

Discrete Dynamics in Nature and Society

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This paper proposes a novel impulsive stochastic nonautonomous chemostat model with the saturated and bilinear growth rates in a polluted environment. Using the theory of impulsive differential equations and Lyapunov functions method, we first investigate the dynamics of the stochastic system and establish the sufficient conditions for the extinction and the permanence of the microorganisms. Then we demonstrate that the stochastic periodic system has at least one nontrivial positive periodic solution. The results show that both impulsive toxicant input and stochastic noise have great effects on the survival and extinction of the microorganisms. Furthermore, a series of numerical simulations are presented to illustrate the performance of the theoretical results.

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Section: Introductionmentioning

confidence: 99%

Dynamics of an Impulsive Stochastic Nonautonomous Chemostat Model with Two Different Growth Rates in a Polluted Environment

Meng

2019

Discrete Dynamics in Nature and Society

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“…With this in mind, the mathematical model of diffusion with pulse has been established, which makes the research more significant [6][7][8][9][10][11][12][13][14]. In particular, impulsive differential equations are very important in the research of population migration phenomenon [15][16][17][18][19][20][21][22][23][24]. Jiao et al [25] established a SIR model with pulse vaccination and proved the existence of a disease-free periodic solution, and a large pulse vaccination rate was a sufficient condition to eradicate the disease.…”

Section: Introductionmentioning

confidence: 99%

Dynamic analysis of unilateral diffusion Gompertz model with impulsive control strategy

Cheng

Wang

et al. 2018

Adv Differ Equ

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In this paper, we establish a unilateral diffusion Gompertz model of a single population in two patches in a theoretical way. Firstly, we prove the existence and uniqueness of an order-one periodic solution by the geometry theory of differential equations and the method of successor function. Secondly, we prove the stability of the order-one periodic solution by imitating the theory of the limit cycle of an ordinary differential equation. Finally, we verify the theoretical results by numerical simulations.

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“…Recently, the inequalities techniques have been widely used to impulsive differential systems [6][7][8][9][10], stochastic differential systems [11][12][13][14][15][16] and impulsive stochastic differential systems [17][18][19][20], thus some new and interesting results have been obtained.…”

Section: Introductionmentioning

confidence: 99%

Application of stochastic inequalities to global analysis of a nonlinear stochastic SIRS epidemic model with saturated treatment function

2018

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In this paper, we propose a new nonlinear stochastic SIRS epidemic model with standard incidence rate and saturated treatment function. The main purpose of this paper is to investigate the threshold dynamics of the nonlinear stochastic SIRS epidemic model by making use of stochastic inequality techniques. By using Lyapunov methods and Itô's formula, we first prove the existence and uniqueness of a global positive solution for the corresponding limiting system. Furthermore, we obtain sufficient conditions for the extinction and persistence in mean of the nonlinear stochastic SIRS epidemic model by using the techniques of a series of stochastic inequalities. Finally, we provide some numerical simulations to illustrate the performance of our theoretical findings.

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Periodic solution of a chemostat model with variable yield and impulsive state feedback control

Cited by 50 publications

References 28 publications

Dynamics of an Impulsive Stochastic Nonautonomous Chemostat Model with Two Different Growth Rates in a Polluted Environment

Dynamics of an Impulsive Stochastic Nonautonomous Chemostat Model with Two Different Growth Rates in a Polluted Environment

Dynamic analysis of unilateral diffusion Gompertz model with impulsive control strategy

Application of stochastic inequalities to global analysis of a nonlinear stochastic SIRS epidemic model with saturated treatment function

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