Dynamics of a model of allelopathy and bacteriocin with a single mutation

作者：Zou, Lan; Chen, Xingwu; Ruan, Shigui^*; Zhang, Weinian

来源：Nonlinear Analysis: Real World Applications , 2011, 12(1): 658-670.

DOI：10.1016/j.nonrwa.2010.07.008

• Population dynamics
• Saddle-node
• Index of equilibrium
• Center manifold
• Bifurcation

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 both microorganisms 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.

• 出版日期2011-2
• 单位四川大学