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The Asymptotic Behavior of Flow Reactor Models with Two Nutrients

注意：本论文已在 Mathematical and Computer Modelling 40 (2004) 465-479发表
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ZHIPENG QIU (邱志鹏)
Department of Mathematics, University of Science and Technology of China
Hefei 230026, P.R. China
and
Department of Applied Mathematics, Nanjing University of Science and Technology
Nanjing 210094, P.R. China

KAIFA WANG
Department of Mathematics, College of Medicine, Third Military Medical University
Chongqing 400038, P.R. China

YUN Zou
Department of Applied Mathematics, Nanjing University of Science and Technology
Nanjing 210094, P.R. China

Abstract: In this paper, the asymptotic behavior of flow reactor models with two nutrients is considered. Different diffusion coefficients of the population and nutrients, the death rates of the population and the velocity existing in the flow reactor are introduced in these models. In complementary case, sufficient conditions for robust persistence and extinction of the population are obtained by the theory of uniform persistence of infinite dimensional dynamical systems. Especially for the model with equal diffusion coefficients and zero death rates, the global attractivity of the unique positive steady-state solution is proved. In substitutable case, sufficient conditions for robust persistence and extinction of population are also obtained by the same method. For the model with equal diffusion coefficients and zero death rates, the uniqueness and global attractivity of the positive steady-state solution is established.
Keywords--Flow reactor model, Two nutrients, Diffusion, Robust persistence.

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1、The Asymptotic Behavior of Flow Reactor Models with Two Nutrients

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