Competition between plasmid-bearing and plasmid-free organisms in a chemostat with nutrient recycling and an inhibitor
- 作者：Sanling Yuan ; Dongmei Xiao and Maoan Han
- 关键词：Chemostat ; Competition ; Nutrient recycling ; Inhibitor ; Uniform persistence
- 刊名：Mathematical Biosciences
- 出版年：2006
- 期刊代码：40_00255564
- 类别：mt
- 出版时间：July 2006
- 卷：202
- 期：1
- 页码：1-28
- 文件大小：327 K
摘要
The asymptotic behavior of solutions of a model for competition between plasmid-bearing and plasmid-free organisms in the chemostat with two distributed delays and an external inhibitor is considered. The model presents a refinement of the one considered by Lu and Hadeler [Z. Lu, K.P. Hadeler, Model of plasmid-bearing plasmid-free competition in the chemostat with nutrient recycling and an inhibitor, Math. Biosci. 167 (2000) p. 177]. The delays model the fact that the nutrient is partially recycled after the death of the biomass by bacterial decomposition. Furthermore, it is assumed that there is inter-specific competition between the plasmid-bearing and plasmid-free organisms as well as intra-specific competition within each population. Conditions for boundedness of solutions and existence of non-negative equilibrium are given. Analysis of the extinction of the organisms, including plasmid-bearing and plasmid-free organisms, and the uniform persistence of the system are also carried out. By constructing appropriate Liapunov-like functionals, some sufficient conditions of global attractivity to the extinction equilibria are obtained and the combined effects of the delays and the inhibitor are studied.