Advances in Difference Equations
Volume 2009 (2009), Article ID 514240, 17 pages
Research Article

A Delayed Chemostat Model with Impulsive Diffusion and Input on Nutrients

Guizhou Key Laboratory of Economic System Simulation, School of Mathematics and Statistics, Guizhou College of Finance and Economics, Guiyang 550004, China

Received 21 August 2009; Revised 2 November 2009; Accepted 30 November 2009

Academic Editor: Binggen Zhang

Copyright © 2009 Jianjun Jiao and Shaohong Cai. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.