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Digital Object Identifier (DOI): 10.1007/s002850000057
 

Summary: Digital Object Identifier (DOI):
10.1007/s002850000057
J. Math. Biol. 42, 7194 (2001)
Mathematical Biology
Shangbing Ai
Periodic solutions in a model of competition between
plasmid-bearing and plasmid-free organisms
in a chemostat with an inhibitor
Received: 20 November 1997 / Revised version: 12 February 1999 /
Published online: 20 December 2000 c Springer-Verlag 2001
Abstract. We obtain necessary and sufficient conditions on the existence of a unique posi-
tive 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].
1. Introduction
In this paper, we consider the existence of positive equilibriums and positive pe-
riodic solutions for a 3-dimensional dynamical system established by Hsu, Luo
and Waltman [1] in studying a model of competition between plasmid-bearing and
plasmid-free organisms in a chemostat with an inhibitor. The physical setting is

  

Source: Ai, Shangbing - Department of Mathematical Sciences, University of Alabama in Huntsville

 

Collections: Mathematics