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

Sze-Bi Hsu; Cheng-Che Li

doi:10.3934/dcdsb.2005.5.699

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2005, Volume 5, Issue 3: 699-718. Doi: 10.3934/dcdsb.2005.5.699

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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
2.
Holistic Education Center, St. John's and St. Mary's Institute of Technology, Tam-Shui 25135

Received: January 31, 2004

Revised: October 31, 2004

Published: July 2005

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Abstract

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.

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Mathematics Subject Classification: 34D05, 34K25, 92D25.

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