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

Lan Zou; Xingwu Chen; Shigui Ruan; Weinian Zhang

doi:10.1016/j.nonrwa.2010.07.008

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

Lan Zou, Xingwu Chen, Shigui Ruan, Weinian Zhang

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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	https://doi.org/10.1016/j.nonrwa.2010.07.008
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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10.1016/j.nonrwa.2010.07.008

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title = "Dynamics of a model of allelopathy and bacteriocin with a single mutation",

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.",

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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

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JO - Nonlinear Analysis: Real World Applications

JF - Nonlinear Analysis: Real World Applications

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

Abstract

Keywords

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