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

Lan Zou, Xingwu Chen, Shigui Ruan, Weinian Zhang

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)658-670
Number of pages13
JournalNonlinear Analysis: Real World Applications
Issue number1
StatePublished - Feb 2011


  • Bifurcation
  • Center manifold
  • Index of equilibrium
  • Population dynamics
  • Saddlenode

ASJC Scopus subject areas

  • Analysis
  • Engineering(all)
  • Economics, Econometrics and Finance(all)
  • Computational Mathematics
  • Applied Mathematics


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