Analysis of a delayed Monod type chemostat model with impulsive input the polluted nutrient

In this paper, a Monod type chemostat model with delayed response in growth and impulsive input the polluted nutrient is considered. Using the discrete dynamical system determined by the stroboscopic map, we obtain a microorganism-extinction periodic solution. Further, it is globally attractive. The permanent condition of the investigated system is also obtained by the theory of impulsive delay differential equation. Our results reveal that the delayed response in growth plays an important role on the outcome of the chemostat.