Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 204632, 17 pages
doi:10.1155/2009/204632
Research Article

Competition between Plasmid-Bearing and Plasmid-Free Organisms in a Chemostat with Pulsed Input and Washout

Sanling Yuan,1 Yu Zhao,1 and Anfeng Xiao2

1College of Science, Shanghai University for Science and Technology, Shanghai 200093, China
2College of Bioengineering, Jimei University, Xiamen 361021, China

Received 5 June 2009; Accepted 11 September 2009

Academic Editor: Bin Liu

Copyright © 2009 Sanling Yuan et al. 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.

Abstract

We consider a model of competition between plasmid-bearing and plasmid-free organisms in the chemostat with pulsed input and washout. We investigate the subsystem with nutrient and plasmid-free organism and study the stability of the boundary periodic solutions, which are the boundary periodic solutions of the system. The stability analysis of the boundary periodic solution yields the invasion threshold of the plasmid-bearing organism. By using the standard techniques of bifurcation theory, we prove that above this threshold there are periodic oscillations in substrate, plasmid-free, and plasmid-bearing organisms. Numerical simulations are carried out to illustrate our results.