Extinction and permanence of two-nutrient and two-microorganism chemostat model with pulsed input

In this paper, a model of the chemostat involving two species of microorganisms competing for two perfectly complementary, growth-limiting nutrients and periodically pulsed input is considered. By using the Floquet’s theorem, we find the two-microorganism eradication periodic solution is globally asymptotically stable if R 1 < 1 . At the same time we can find nutrients and microorganisms are permanent if R 2 > 1 . Meanwhile, sufficient conditions based on biologically meaningful parameters in the model are given that predict competitive exclusion for certain parameter ranges and coexistence for others. Finally, our results are illustrated by numerical simulation.