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.

中文翻译：

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具有单一突变的化感作用和细菌素模型的动力学。


在本文中，我们讨论了具有野生型生物体和单一突变体的恒化器中的化感作用和细菌素模型。该模型的动力学特性显示了两种微生物之间的基本竞争。对边界平衡（微生物都消失的状态）进行了定性分析。内部均衡的存在性和唯一性通过对矩阵奇点的技术还原来证明。利用平衡指数理论给出了其动力学性质。我们进一步讨论它的分歧。我们的结果通过数值模拟得到了证明。