Dynamical behaviors of a delayed chemostat model with impulsive diffusion on nutrients

In this paper, a chemostat model with delayed response in growth and impulsive diffusion on nutrients 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 on impulsive delay differential equation. Our results reveal that the impulsive diffusion amount plays an important role on the outcome of the chemostat. Finally, the numerical analysis is inserted to illustrate the results.