Some new results on an allelopathic competition model with quorum sensing and delayed toxicant production

P. Fergola; E. Beretta; M. Cerasuolo

doi:10.1016/j.nonrwa.2005.10.001

Some new results on an allelopathic competition model with quorum sensing and delayed toxicant production

P. Fergola^*, E. Beretta, M. Cerasuolo

^*Corresponding author for this work

School of Mathematics & Physics

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

Abstract

A 4-equation delay differential system representing a bacterial allelopathic competition is analyzed. A distributed delay term models a linear quorum-sensing mechanism which regulates the delayed allelochemicals' production process. The proved qualitative properties of the solutions are positivity, boundedness, global existence in the future, and uniqueness. Sufficient conditions for local asymptotic stability properties of biologically meaningful steady-state solutions are given in terms of the parameters of the system. The global asymptotic stability of a biologically meaningful steady-state solution is proved by constructing a suitable Lyapunov functional.

Original language	English
Pages (from-to)	1081-1095
Number of pages	15
Journal	Nonlinear Analysis: Real World Applications
Volume	7
Issue number	5
DOIs	https://doi.org/10.1016/j.nonrwa.2005.10.001
Publication status	Published - 1 Dec 2006

Keywords

Allelopathy
Chemostat models
Distributed delay
Global stability
Quorum sensing

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10.1016/j.nonrwa.2005.10.001

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title = "Some new results on an allelopathic competition model with quorum sensing and delayed toxicant production",

abstract = "A 4-equation delay differential system representing a bacterial allelopathic competition is analyzed. A distributed delay term models a linear quorum-sensing mechanism which regulates the delayed allelochemicals' production process. The proved qualitative properties of the solutions are positivity, boundedness, global existence in the future, and uniqueness. Sufficient conditions for local asymptotic stability properties of biologically meaningful steady-state solutions are given in terms of the parameters of the system. The global asymptotic stability of a biologically meaningful steady-state solution is proved by constructing a suitable Lyapunov functional.",

keywords = "Allelopathy, Chemostat models, Distributed delay, Global stability, Quorum sensing",

author = "P. Fergola and E. Beretta and M. Cerasuolo",

year = "2006",

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doi = "10.1016/j.nonrwa.2005.10.001",

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TY - JOUR

T1 - Some new results on an allelopathic competition model with quorum sensing and delayed toxicant production

AU - Fergola, P.

AU - Beretta, E.

AU - Cerasuolo, M.

PY - 2006/12/1

Y1 - 2006/12/1

N2 - A 4-equation delay differential system representing a bacterial allelopathic competition is analyzed. A distributed delay term models a linear quorum-sensing mechanism which regulates the delayed allelochemicals' production process. The proved qualitative properties of the solutions are positivity, boundedness, global existence in the future, and uniqueness. Sufficient conditions for local asymptotic stability properties of biologically meaningful steady-state solutions are given in terms of the parameters of the system. The global asymptotic stability of a biologically meaningful steady-state solution is proved by constructing a suitable Lyapunov functional.

AB - A 4-equation delay differential system representing a bacterial allelopathic competition is analyzed. A distributed delay term models a linear quorum-sensing mechanism which regulates the delayed allelochemicals' production process. The proved qualitative properties of the solutions are positivity, boundedness, global existence in the future, and uniqueness. Sufficient conditions for local asymptotic stability properties of biologically meaningful steady-state solutions are given in terms of the parameters of the system. The global asymptotic stability of a biologically meaningful steady-state solution is proved by constructing a suitable Lyapunov functional.

KW - Allelopathy

KW - Chemostat models

KW - Distributed delay

KW - Global stability

KW - Quorum sensing

UR - http://www.scopus.com/inward/record.url?scp=33745181919&partnerID=8YFLogxK

UR - https://www.sciencedirect.com/journal/nonlinear-analysis-real-world-applications/vol/7/issue/5

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DO - 10.1016/j.nonrwa.2005.10.001

M3 - Article

AN - SCOPUS:33745181919

SN - 1468-1218

VL - 7

SP - 1081

EP - 1095

JO - Nonlinear Analysis: Real World Applications

JF - Nonlinear Analysis: Real World Applications

IS - 5

ER -

Some new results on an allelopathic competition model with quorum sensing and delayed toxicant production

Abstract

Keywords

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