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Study of two-nutrient and two-micro-organism chemostat model with pulsed input in a polluted environment

Jianwen Jia

School of Mathematics and Computer Science, Shanxi Normal University, Shanxi, Linfen 041004, P. R. China

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and

Tingting Lv

School of Mathematics and Computer Science, Shanxi Normal University, Shanxi, Linfen 041004, P. R. China

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https://doi.org/10.1142/S1793524515500424Cited by:2 (Source: Crossref)

Abstract

In this paper, a model of Beddington–DeAngelies chemostat involving two species of micro-organism competing for two perfectly complementary growth-limiting nutrients and pulsed input of toxicant in the polluted environment was studied. Using Floquet theory and small amplitude perturbation method, a conclusion was that there exists two-micro-organism eradication periodic solution and which is global asymptotical stability. At the same time, the condition of the permanence for system was obtained. From the biological point of view, the method for protecting species is to improve the amount of impulsive period, and control the amount of toxicant input to the chemostat. Finally, our results are illustrated by numerical simulations.

Keywords:

AMSC: 34K45, 34C25, 92D25

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