Global qualitative analysis of new Monod type chemostat model with delayed growth response and pulsed input in polluted environment

2008 ◽  
Vol 29 (1) ◽  
pp. 75-87 ◽  
Author(s):  
Xin-zhu Meng ◽  
Qiu-lan Zhao ◽  
Lan-sun Chen
Keyword(s):  
Qualitative Analysis ◽  
Growth Response ◽  
Polluted Environment ◽  
Chemostat Model ◽  
Delayed Growth

Analysis of a Crowley-Martin Type Chemostat with Delayed Growth Response and Pulsed Input

2014 ◽  
Vol 556-562 ◽  
pp. 4333-4337
Author(s):  
Ming Juan Sun ◽  
Hua Xin Zhao ◽  
Qing Lai Dong
Keyword(s):  
Differential Equation ◽  
Growth Response ◽  
Global Attractivity ◽  
Computational Techniques ◽  
Chemostat Model ◽  
Delayed Differential Equation ◽  
Delayed Growth

In this paper, we introduce and study a Crowley-Martin type Chemostat model with delayed growth response and pulsed input. We get that the existence and the global attractivity of a ‘microorganism-extinction’periodic solution. We prove that the system is permanent under appropriate conditions, by use of new computational techniques for impulsive and delayed differential equation.

Qualitative analysis of a chemostat model with inhibitory exponential substrate uptake and a time delay

2014 ◽  
Vol 07 (04) ◽  
pp. 1450045 ◽  
Author(s):  
Qinglai Dong ◽  
Wanbiao Ma
Keyword(s):  
Time Delay ◽  
Asymptotic Stability ◽  
Qualitative Analysis ◽  
Numerical Simulations ◽  
Global Asymptotic Stability ◽  
Positive Equilibrium ◽  
Substrate Uptake ◽  
Sufficient Condition ◽  
Chemostat Model ◽  
Local Asymptotic Stability

In this paper, we consider a simple chemostat model with inhibitory exponential substrate uptake and a time delay. A detailed qualitative analysis about existence and boundedness of its solutions and the local asymptotic stability of its equilibria are carried out. Using Lyapunov–LaSalle invariance principle, we show that the washout equilibrium is global asymptotic stability for any time delay. Using the fluctuation lemma, the sufficient condition of the global asymptotic stability of the positive equilibrium [Formula: see text] is obtained. Numerical simulations are also performed to illustrate the results.

scholarly journals On the Study of Chemostat Model with Pulsed Input in a Polluted Environment

2007 ◽  
Vol 2007 ◽  
pp. 1-12 ◽  
Author(s):  
Zhong Zhao ◽  
Xinyu Song
Keyword(s):  
Periodic Solution ◽  
Critical Value ◽  
Asymptotically Stable ◽  
Polluted Environment ◽  
Chemostat Model ◽  
Globally Asymptotically Stable ◽  
Floquet Theorem

Chemostat model with pulsed input in a polluted environment is considered. By using the Floquet theorem, we find that the microorganism eradication periodic solution is globally asymptotically stable if the impulsive periodTis more than a critical value. At the same time, we can find that the nutrient and microorganism are permanent if the impulsive periodTis less than the critical value.

Qualitative Analysis of a Ratio-Dependent Chemostat Model with Holling-(n+1) Type Functional Response

2013 ◽  
Vol 641-642 ◽  
pp. 947-950
Author(s):  
Qing Lai Dong ◽  
Ming Juan Sun
Keyword(s):  
Asymptotic Stability ◽  
Qualitative Analysis ◽  
Functional Response ◽  
Global Asymptotic Stability ◽  
Monod Model ◽  
Chemostat Model ◽  
Dependent Model ◽  
Ratio Dependent ◽  
Lasalle Invariant Principle ◽  
Invariant Principle

In this paper, the ratio-dependent chemostat model with Holling-(n+1) type functional response is considered. The model develops the Monod model and the ratio-dependent model. By use of the Poincar -Bendixson theory we prove the existence of limit cycle. Detailed qualitative analysis about the global asymptotic stability of its equilibria is carried out by using the Lyapunov-LaSalle invariant principle and the method of Dulac criterion.

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

2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Yajie Li ◽  
Xinzhu Meng
Keyword(s):  
Growth Rates ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Positive Periodic Solution ◽  
Stochastic Noise ◽  
Polluted Environment ◽  
Chemostat Model ◽  
Lyapunov Functions Method ◽  
Theoretical Results

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.

Transient oscillations induced by delayed growth response in the chemostat

2005 ◽  
Vol 50 (5) ◽  
pp. 489-530 ◽  
Author(s):  
Huaxing Xia ◽  
Gail S.K. Wolkowicz ◽  
Lin Wang
Keyword(s):  
Growth Response ◽  
Delayed Growth ◽  
Transient Oscillations
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