American Institute of Mathematical Sciences

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August  2005, 5(3): 699-718. doi: 10.3934/dcdsb.2005.5.699

A discrete-delayed model with plasmid-bearing, plasmid-free competition in a chemostat

Sze-Bi Hsu 1, and  Cheng-Che Li 2,

1. 

Department of Mathematics, National Tsing-Hua University, Hsin-Chu 30043, Taiwan
2. 

Holistic Education Center, St. John's and St. Mary's Institute of Technology, Tam-Shui 25135, Taiwan

Received  February 2004 Revised  November 2004 Published  May 2005

A discrete-delayed model of plasmid-bearing, plasmid-free organisms competing for a single-limited nutrient in a chemostat is established. Rigorous mathematical analysis of the asymptotic behavior of this model is presented. An interesting method to analyze the local stability of interior equilibrium is developed. The argument is also applicable to a model of plasmid-bearing, plasmid-free organisms competing for two complementary nutrients in a chemostat.
Keywords: chemostat, plasmid-bearing, global attractivity., plasmid-free, Delayed growth response, perturbation.
Mathematics Subject Classification: 34D05, 34K25, 92D2.
Citation: Sze-Bi Hsu, Cheng-Che Li. A discrete-delayed model with plasmid-bearing, plasmid-free competition in a chemostat. Discrete and Continuous Dynamical Systems - B, 2005, 5 (3) : 699-718. doi: 10.3934/dcdsb.2005.5.699
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