ANALYSIS OF A MODEL OF PLASMID-BEARING, PLASMID-FREE COMPETITION IN A PULSED CHEMOSTAT

Xiangyun Shi (), Xinyu Song () and Xueyong Zhou
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Xiangyun Shi: Department of Mathematics, Xinyang Normal University, Xinyang 464000, Henan, China
Xinyu Song: Department of Mathematics, Xinyang Normal University, Xinyang 464000, Henan, China
Xueyong Zhou: Department of Mathematics, Xinyang Normal University, Xinyang 464000, Henan, China

Advances in Complex Systems (ACS), 2006, vol. 09, issue 03, 263-276

Abstract: We introduce and study a chemostat model with plasmid-bearing, plasmid-free competition and impulsive effect. According to the stability analysis of the boundary periodic solution, we obtain the invasion threshold of the plasmid-free organism and plasmid-bearing organism. Furthermore, by using standard techniques of bifurcation theory, we prove the system has a positive τ-periodic solution, which shows that the impulsive effect destroys the equilibria of the unforced continuous system and initiates the periodic solution. Our results can be applied to control bioreactors aimed at producing commercial products through genetically altered organisms.

Keywords: Chemostat model; impulsive effect; periodic solution; globally asymptotic stability (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1142/S0219525906000768

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