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

Original Paper

DOI: 10.1007/s10910-009-9536-2

Cite this article as:
Meng, X., Li, Z. & Nieto, J.J. J Math Chem (2010) 47: 123. doi:10.1007/s10910-009-9536-2


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.


Permanence Impulsive input Michaelis–Menten type chemostat model Time delay for growth response Extinction 

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Information SchoolShandong University of Science and TechnologyQingdaoPeople’s Republic of China
  2. 2.State Key Laboratory of Vegetation and Environmental Change, Institute of BotanyChinese Academy of SciencesBeijingPeople’s Republic of China
  3. 3.Departamento de Análisis Matemático, Facultad de MatemáticasUniversidad de Santiago de CompostelaSantiago de CampostelaSpain

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