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

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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

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

Abstract
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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 & Continuous Dynamical Systems - B, 2005, 5 (3) : 699-718. doi: 10.3934/dcdsb.2005.5.699

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