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

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

Kaifa Wang 1, and  Aijun Fan 1,

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.
Keywords: periodic solution., Antibiotic, uniform persistence.
Mathematics Subject Classification: 34C25, 92D2.
Citation: Kaifa Wang, Aijun Fan. Uniform persistence and periodic solution of chemostat-type model with antibiotic. Discrete and Continuous Dynamical Systems - B, 2004, 4 (3) : 789-795. doi: 10.3934/dcdsb.2004.4.789
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