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

Lan Zou, Xingwu Chen, Shigui Ruan, Weinian Zhang

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 languageEnglish (US)
Pages (from-to)658-670
Number of pages13
JournalNonlinear Analysis: Real World Applications
Volume12
Issue number1
DOIs
StatePublished - Feb 2011

Fingerprint

Allelopathy
Bacteriocins
Microorganisms
Mutation
Chemostats
Chemostat
Index Theory
Qualitative Analysis
Mutant
Vanish
Computer simulation
Interior
Existence and Uniqueness
Bifurcation
Model
Singularity
Numerical Simulation

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 journalArticle

@article{2d1045a31b8749138724764b80e83167,
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.",
keywords = "Bifurcation, Center manifold, Index of equilibrium, Population dynamics, Saddlenode",
author = "Lan Zou and Xingwu Chen and Shigui Ruan and Weinian Zhang",
year = "2011",
month = "2",
doi = "10.1016/j.nonrwa.2010.07.008",
language = "English (US)",
volume = "12",
pages = "658--670",
journal = "Nonlinear Analysis: Real World Applications",
issn = "1468-1218",
publisher = "Elsevier BV",
number = "1",

}

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 -