Dynamics of a Model of Allelopathy and Bacteriocin with a Single Mutation |
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Authors: | Zou Lan Chen Xingwu Ruan Shigui Zhang Weinian |
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Affiliation: | Yangtze Center of Mathematics and Departmant of Mathematics Sichuan University, Chengdu, Sichuan 610064, P. R. China. |
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Abstract: | 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. |
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