A delayed chemostat model with impulsive diffusion and input on nutrients

Abstract

A chemostat model with delayed response in growth and impulsive diffusion and input 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. Finally, numerical analysis is inserted to illustrate dynamical behaviors of the chemostat system. Our results reveal that the impulsive input amount of nutrients plays an important role on the outcome of the chemostat. Our results provide strategy basis for biochemical reaction management. © 2009 J. Jiao and S. Cai.