Study of chemostat model with impulsive input and nutrient recycling in a polluted environment

In this paper, we introduce and study a Monod type chemostat model with nutrient recycling and impulsive input in a polluted environment. The sufficient and necessary conditions on the permanence and extinction of the microorganism are obtained. Two examples are given in the last section to verify our mathematical results. The numerical analysis show that if only the system is permanent, then it also is globally attractive.