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Extinction and permanence of chemostat model with pulsed input in a polluted environment. (English) Zbl 1221.37209

Summary: A chemostat model with pulsed input in a polluted environment is considered. By using the Floquet theorem, we find the microorganism eradication periodic solution is globally asymptotically stable if some conditions are needed. At the same time we can find the condition of the nutrient and microorganism are permanent.

MSC:

37N25 Dynamical systems in biology
34D05 Asymptotic properties of solutions to ordinary differential equations
92D25 Population dynamics (general)
34D20 Stability of solutions to ordinary differential equations
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