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 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 language | English (US) |
|---|---|
| Pages (from-to) | 658-670 |
| Number of pages | 13 |
| Journal | Nonlinear Analysis: Real World Applications |
| Volume | 12 |
| Issue number | 1 |
| DOIs | |
| State | Published - Feb 2011 |
Keywords
- 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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Cite this
Zou, L., Chen, X., Ruan, S., & Zhang, W. (2011). Dynamics of a model of allelopathy and bacteriocin with a single mutation. Nonlinear Analysis: Real World Applications, 12(1), 658-670. https://doi.org/10.1016/j.nonrwa.2010.07.008