Stability Analysis of a Ratio-Dependent Chemostat Model withVariable Yield and Time Delay
DONG Qinglai(1)(2), MA Wanbiao(1)
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(1)Department of Mathematics and Mechanics, School of Applied Science University of Science and Technology Beijing, Beijing 100083; (2)School of Mathematics and Computer Science, Yan'an University, Yan'an 716000
In this paper, based on some biological meanings, a class of ratio-dependent Chemostat model with variable yield and time delay is considered. In the Chemostat model, time delay is introduced into growth response of microbial population. Firstly, a detailed theoretical analysis about existence and boundedness of the solutions and local asymptotic stability of the equilibria are carried out, and the Hopf bifurcation is also studied. Then by using classical Lyapunov-LaSalle invariance principle, it is shown that the washout equilibrium (i.e., boundary equilibrium) is globally asymptotically stable for any time delay. Finally, it is shown that the Chemostat model is uniformly persistent for any time delay.
DONG Qinglai
, MA Wanbiao. , {{custom_author.name_en}}.
Stability Analysis of a Ratio-Dependent Chemostat Model withVariable Yield and Time Delay. Journal of Systems Science and Mathematical Sciences, 2009, 29(2): 228-241 https://doi.org/10.12341/jssms10085
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