Journal of Mathematical Biology

, Volume 42, Issue 1, pp 71-94

Periodic solutions in a model of competition between plasmid-bearing and plasmid-free organisms in a chemostat with an inhibitor

  • Shangbing AiAffiliated withDepartment of Mathematics, University of Pittsburgh, Pittsburgh, PA 15216, USA. e-mail: sxast10@math.pitt.edu

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Abstract.

We obtain necessary and sufficient conditions on the existence of a unique positive equilibrium point and a set of sufficient conditions on the existence of periodic solutions for a 3-dimensional system which arises from a model of competition between plasmid-bearing and plasmid-free organisms in a chemostat with an inhibitor. Our results improve the corresponding results obtained by Hsu, Luo, and Waltman [1].

Key words: Chemostat – Periodic solution – Brouwer fixed point theorem