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 |
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Keywords
- Bifurcation
- Center manifold
- Index of equilibrium
- Population dynamics
- Saddlenode
ASJC Scopus subject areas
- Analysis
- Applied Mathematics
- Computational Mathematics
- Engineering(all)
- Medicine(all)
- Economics, Econometrics and Finance(all)
Cite this
Dynamics of a model of allelopathy and bacteriocin with a single mutation. / Zou, Lan; Chen, Xingwu; Ruan, Shigui; Zhang, Weinian.
In: Nonlinear Analysis: Real World Applications, Vol. 12, No. 1, 02.2011, p. 658-670.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Dynamics of a model of allelopathy and bacteriocin with a single mutation
AU - Zou, Lan
AU - Chen, Xingwu
AU - Ruan, Shigui
AU - Zhang, Weinian
PY - 2011/2
Y1 - 2011/2
N2 - 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.
AB - 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.
KW - Bifurcation
KW - Center manifold
KW - Index of equilibrium
KW - Population dynamics
KW - Saddlenode
UR - http://www.scopus.com/inward/record.url?scp=77958003925&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77958003925&partnerID=8YFLogxK
U2 - 10.1016/j.nonrwa.2010.07.008
DO - 10.1016/j.nonrwa.2010.07.008
M3 - Article
AN - SCOPUS:77958003925
VL - 12
SP - 658
EP - 670
JO - Nonlinear Analysis: Real World Applications
JF - Nonlinear Analysis: Real World Applications
SN - 1468-1218
IS - 1
ER -