Analysis of a chemostat model with pulsed input

In this paper, we consider a chemostat model with pulsed input. We find a critical value of the period of pulses. If the period is more than the critical value, the microorganism-free periodic solution is globally asymptotically stable. If less, the system is permanent. Moreover, the nutrient and the microorganism can co-exist on a periodic solution of period tau. Finally, by comparing the corresponding continuous system, we find that the periodically pulsed input destroys the equilibria of the continuous system and initiates periodic solutions. Our results are valuable for the manufacture of products by genetically altered organisms.