Original Paper

Journal of Mathematical Chemistry

, Volume 47, Issue 1, pp 123-144

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

  • Xinzhu MengAffiliated withInformation School, Shandong University of Science and TechnologyState Key Laboratory of Vegetation and Environmental Change, Institute of Botany, Chinese Academy of Sciences
  • , Zhenqing LiAffiliated withState Key Laboratory of Vegetation and Environmental Change, Institute of Botany, Chinese Academy of Sciences Email author 
  • , Juan J. NietoAffiliated withDepartamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela

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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.

Keywords

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