Impulsive control of a continuous-culture and flocculation harvest chemostat model

Zhang, Tongqian; Ma, Wanbiao; Meng, Xinzhu

doi:10.1080/00207721.2017.1384861

Cited by 8 publications

(3 citation statements)

References 45 publications

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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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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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“…And due to the seasonal and economic reasons, periodic harvesting is an effective harvesting strategy for the infrequent harvesting. This periodic harvesting can be described by impulsive differential equations [9][10][11][12][13][14][15][16]. There are some papers studying the effects of periodic impulse harvesting strategy to the species resource.…”

Section: Introductionmentioning

confidence: 99%

Periodic solution and control optimization of a prey-predator model with two types of harvesting

et al. 2018

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In this work, a prey-predator model with both state-dependent impulsive harvesting and constant rate harvesting is investigated, where the replenishment rate of prey and the harvesting rate are linearly related with the selected threshold. By first using the successor function method and differential equation geometry theory, the existence, uniqueness and asymptotic stability of the order-1 periodic solution are discussed. And then numerical simulations with an example are given to illustrate the feasibility of the theorem-related results. Moreover, in order to increase the total profit, the optimization strategy is presented and the optimal threshold is obtained.

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“…The Lotka-Volterra model [1][2][3] is a classical model in the study of biological mathematics, and the continuous LotkaVolterra model which is modeled by ordinary differential equations and delay differential equations is widely used to characterize the dynamics of biological systems [4][5][6][7][8][9][10][11][12][13]. The functional response functions are important in the population ecological models [14].…”

Section: Introduction and Model Formulationmentioning

confidence: 99%

Dynamical Analysis of a Class of Prey-Predator Model with Beddington-DeAngelis Functional Response, Stochastic Perturbation, and Impulsive Toxicant Input

et al. 2017

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A stochastic prey-predator system in a polluted environment with Beddington-DeAngelis functional response is proposed and analyzed. Firstly, for the system with white noise perturbation, by analyzing the limit system, the existence of boundary periodic solutions and positive periodic solutions is proved and the sufficient conditions for the existence of boundary periodic solutions and positive periodic solutions are derived. And then for the stochastic system, by introducing Markov regime switching, the sufficient conditions for extinction or persistence of such system are obtained. Furthermore, we proved that the system is ergodic and has a stationary distribution when the concentration of toxicant is a positive constant. Finally, two examples with numerical simulations are carried out in order to illustrate the theoretical results.

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Impulsive control of a continuous-culture and flocculation harvest chemostat model

Cited by 8 publications

References 45 publications

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

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

Periodic solution and control optimization of a prey-predator model with two types of harvesting

Dynamical Analysis of a Class of Prey-Predator Model with Beddington-DeAngelis Functional Response, Stochastic Perturbation, and Impulsive Toxicant Input

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