Stationary distribution of a stochastic chemostat model with Beddington–DeAngelis functional response

2020 ◽  
Vol 554 ◽  
pp. 124634
Author(s):  
Zhongwei Cao ◽  
Xiangdan Wen ◽  
Huishuang Su ◽  
Liya Liu ◽  
Qiang Ma
Keyword(s):  
Functional Response ◽  
Stationary Distribution ◽  
Chemostat Model

Asymptotic Behavior of a Chemostat Model with Watt Type Functional Response and Variable Yield

2013 ◽  
Vol 423-426 ◽  
pp. 1496-1500
Author(s):  
Qing Lai Dong ◽  
Ming Juan Sun
Keyword(s):  
Asymptotic Behavior ◽  
Hopf Bifurcation ◽  
Theoretical Analysis ◽  
Continuous Culture ◽  
Functional Response ◽  
Limit Cycles ◽  
Microbial Growth ◽  
Global Asymptotical Stability ◽  
Chemostat Model ◽  
Variable Yield

To make the theoretical analysis of the microbial continuous culture more close to the experimental results, we consider a chemostat model with Watt type functional response and variable yield. The existence of limit cycles and Hopf bifurcation is investigated, which is useful in the further study of the oscillatory behaviors of the microbial growth in the vessel. The conditions for the global asymptotical stability of the model are obtained by Dulac criterion.

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.

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