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Dynamic analysis of Michaelis-Menten chemostat-type competition models with time delay and pulse in a polluted environment. (English) Zbl 1194.92075

Summary: 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 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.

MSC:

92D40 Ecology
34K45 Functional-differential equations with impulses
92-08 Computational methods for problems pertaining to biology
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