American Institute of Mathematical Sciences

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August  2004, 4(3): 721-727. doi: 10.3934/dcdsb.2004.4.721

The asymptotic behavior of a chemostat model

Zhipeng Qiu 1, , Jun Yu 1, and  Yun Zou 2,

1. 

Department of Mathematics, University of Science and Technology of China, Hefei 230026, China, China
2. 

Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094, China

Received  October 2002 Revised  January 2004 Published  May 2004

In this paper, the Chemostat model with stage-structure and the Beddington-DeAngelies functional responses is studied. Sufficient conditions for uniform persistence of this model with delay are obtained via uniform persistence of infinite dimensional dynamical systems; and for the model without delay, sufficient conditions for the global asymptotic stability of the positive equilibrium are presented.
Keywords: global asymptotic stability, uniform persistence, stage-structure, Chemostat, mutual interference..
Mathematics Subject Classification: 92D2.
Citation: Zhipeng Qiu, Jun Yu, Yun Zou. The asymptotic behavior of a chemostat model. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 721-727. doi: 10.3934/dcdsb.2004.4.721
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