The asymptotic behavior of flowreactor models with two nutrients

Authors:
Zhipeng Qiu;Kaifa Wang;Yun Zou
Affiliations:
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 TechnologyNanjing 210094, ...;Department of Mathematics, College of Medicine, Third Military Medical UniversityChongging 400038, P.R. China;Department of Applied Mathematics, Nanjing University of Science and TechnologyNanjing 210094, P.R. China
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2004

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Abstract

In this paper, the asymptotic behavior of flow reactor models with two nutrientsis 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.