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

XIANGYUN SHI

Department of Mathematics, Xinyang Normal University, Xinyang 464000, Henan, China

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XINYU SONG

Department of Mathematics, Xinyang Normal University, Xinyang 464000, Henan, China

Corresponding author.

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, and

XUEYONG ZHOU

Department of Mathematics, Xinyang Normal University, Xinyang 464000, Henan, China

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https://doi.org/10.1142/S0219525906000768Cited by:3 (Source: Crossref)

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.

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