# American Institute of Mathematical Sciences

August  2004, 4(3): 789-795. doi: 10.3934/dcdsb.2004.4.789

## Uniform persistence and periodic solution of chemostat-type model with antibiotic

 1 Department of Mathematics, College of Medicine, Third Military Medical University, Chongqing, 400038, China, China

Received  December 2002 Revised  January 2004 Published  May 2004

A system of functional differential equations is used to model the single microorganism in the chemostat environment with a periodic nutrient and antibiotic input. Based on the technique of Razumikhin, we obtain the sufficient condition for uniform persistence of the microbial population. For general periodic functional differential equations, we obtain a sufficient condition for the existence of periodic solution, therefore, the existence of positive periodic solution to the chemostat-type model is verified.
Citation: Kaifa Wang, Aijun Fan. Uniform persistence and periodic solution of chemostat-type model with antibiotic. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 789-795. doi: 10.3934/dcdsb.2004.4.789
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