Dynamics of a Model of Allelopathy and Bacteriocin with a Single Mutation.
In this paper we discuss a model of allelopathy and bacteriocin in the chemostat with a wild-type organism and a single mutant. Dynamical properties of this model show the basic competition between two microorganisms. A qualitative analysis about the boundary equilibrium, a state that microorganisms both vanish, is carried out. The existence and uniqueness of the interior equilibrium are proved by a technical reduction to the singularity of a matrix. Its dynamical properties are given by using the index theory of equilibria. We further discuss its bifurcations. Our results are demonstrated by numerical simulations.
Yangtze Center of Mathematics and Departmant of Mathematics Sichuan University, Chengdu, Sichuan 610064, P. R. China.
Lan
L
Zou
Xingwu
X
Chen
Shigui
S
Ruan
Weinian
W
Zhang