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Dynamic analysis of Michaelis–Menten chemostat-type competition models with time delay and pulse in a polluted environment

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Abstract

In this paper, a new Michaelis–Menten type chemostat model with time delay and pulsed input nutrient concentration in a polluted environment is considered. We obtain a ‘microorganism-extinction’ semi-trivial periodic solution and establish the sufficient conditions for the global attractivity of the semi-trivial periodic solution. By use of new computational techniques for impulsive differential equations with delay, we prove and support with numerical calculations that the system is permanent. Our results show that time delays and the polluted environment can lead the microorganism species to be extinct.

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Authors and Affiliations

  1. Information School, Shandong University of Science and Technology, Qingdao, 266510, People’s Republic of China

    Xinzhu Meng

  2. State Key Laboratory of Vegetation and Environmental Change, Institute of Botany, Chinese Academy of Sciences, Beijing, 100093, People’s Republic of China

    Xinzhu Meng & Zhenqing Li

  3. Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, 15782, Santiago de Campostela, Spain

    Juan J. Nieto

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  1. Xinzhu Meng
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  2. Zhenqing Li
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  3. Juan J. Nieto
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Correspondence to Zhenqing Li.

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Meng, X., Li, Z. & Nieto, J.J. Dynamic analysis of Michaelis–Menten chemostat-type competition models with time delay and pulse in a polluted environment. J Math Chem 47, 123–144 (2010). https://doi.org/10.1007/s10910-009-9536-2

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  • DOI: https://doi.org/10.1007/s10910-009-9536-2

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