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Global qualitative analysis of new Monod type chemostat model with delayed growth response and pulsed input in polluted environment

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Abstract

In this paper, we consider a new Monod type chemostat model with time delay and impulsive input concentration of the nutrient in a polluted environment. Using the discrete dynamical system determined by the stroboscopic map, we obtain a “microorganism-extinction” periodic solution. Further, we establish the sufficient conditions for the global attractivity of the microorganism-extinction periodic solution. Using new computational techniques for impulsive and delayed differential equation, we prove that the system is permanent under appropriate conditions. Our results show that time delay is “profitless”.

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Authors and Affiliations

  1. College of Science, Shandong University of Science and Technology, Qingdao, 266510, Shandong Province, P. R. China

    Meng Xin-zhu  (孟新柱) & Zhao Qiu-lan  (赵秋兰)

  2. Department of Applied Mathematics, Dalian University of Technology, Dalian, 116024, Liaoning Province, P. R. China

    Meng Xin-zhu  (孟新柱) & Chen Lan-sun  (陈兰荪)

  3. Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100080, P. R. China

    Chen Lan-sun  (陈兰荪)

Authors
  1. Meng Xin-zhu  (孟新柱)
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  2. Zhao Qiu-lan  (赵秋兰)
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  3. Chen Lan-sun  (陈兰荪)
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Corresponding author

Correspondence to Meng Xin-zhu  (孟新柱).

Additional information

Communicated by GUO Xing-ming

Project supported by the National Natural Science Foundation of China (Nos. 10471117 and 10771179) and the Natural Science Foundation of Shandong University of Science and Technology (No. 05g016)

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Meng, Xz., Zhao, Ql. & Chen, Ls. Global qualitative analysis of new Monod type chemostat model with delayed growth response and pulsed input in polluted environment. Appl. Math. Mech.-Engl. Ed. 29, 75–87 (2008). https://doi.org/10.1007/s10483-008-0110-x

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  • DOI: https://doi.org/10.1007/s10483-008-0110-x

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2000 Mathematics Subject Classification

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