Stability and bifurcation in plant-pathogens interactions

Bruno Buonomo; Marianna Cerasuolo

doi:10.1016/j.amc.2014.01.127

Stability and bifurcation in plant-pathogens interactions

Bruno Buonomo, Marianna Cerasuolo

School of Mathematics & Physics

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Abstract

We consider a plant–pathogen interaction model and perform a bifurcation analysis at the threshold where the pathogen-free equilibrium loses its hyperbolicity. We show that a stimulatory–inhibitory host response to infection load may be responsible for the occurrence of multiple steady states via backward bifurcations. We also find sufficient conditions for the global stability of the pathogen-present equilibrium in case of null or linear inhibitory host response. The results are discussed in the framework of the recent literature on the subject.

Original language	English
Pages (from-to)	858-871
Journal	Applied Mathematics and Computation
Volume	232
Early online date	16 Feb 2014
DOIs	https://doi.org/10.1016/j.amc.2014.01.127
Publication status	Published - 1 Apr 2014

Keywords

Plant–pathogen interaction
Mathematical model
Bifurcation
Global stability

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10.1016/j.amc.2014.01.127

Plant-Pathogen interactions
“NOTICE: this is the author’s version of a work that was accepted for publication in Applied Mathematics and Computation. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Applied Mathematics and Computation, [VOL232, (1/4/14)] DOI10.1016/j.amc.2014.01.127
Accepted author manuscript (Post-print), 431 KBLicence: CC BY

http://www.sciencedirect.com/science/article/pii/S0096300314001726

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title = "Stability and bifurcation in plant-pathogens interactions",

abstract = "We consider a plant–pathogen interaction model and perform a bifurcation analysis at the threshold where the pathogen-free equilibrium loses its hyperbolicity. We show that a stimulatory–inhibitory host response to infection load may be responsible for the occurrence of multiple steady states via backward bifurcations. We also find sufficient conditions for the global stability of the pathogen-present equilibrium in case of null or linear inhibitory host response. The results are discussed in the framework of the recent literature on the subject.",

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AU - Buonomo, Bruno

AU - Cerasuolo, Marianna

N1 - “NOTICE: this is the author’s version of a work that was accepted for publication in <Journal title>. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Applied Mathematics and Computation, [VOL232, (1/4/14)] DOI10.1016/j.amc.2014.01.127

PY - 2014/4/1

Y1 - 2014/4/1

N2 - We consider a plant–pathogen interaction model and perform a bifurcation analysis at the threshold where the pathogen-free equilibrium loses its hyperbolicity. We show that a stimulatory–inhibitory host response to infection load may be responsible for the occurrence of multiple steady states via backward bifurcations. We also find sufficient conditions for the global stability of the pathogen-present equilibrium in case of null or linear inhibitory host response. The results are discussed in the framework of the recent literature on the subject.

AB - We consider a plant–pathogen interaction model and perform a bifurcation analysis at the threshold where the pathogen-free equilibrium loses its hyperbolicity. We show that a stimulatory–inhibitory host response to infection load may be responsible for the occurrence of multiple steady states via backward bifurcations. We also find sufficient conditions for the global stability of the pathogen-present equilibrium in case of null or linear inhibitory host response. The results are discussed in the framework of the recent literature on the subject.

KW - Plant–pathogen interaction

KW - Mathematical model

KW - Bifurcation

KW - Global stability

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DO - 10.1016/j.amc.2014.01.127

M3 - Article

SN - 0096-3003

VL - 232

SP - 858

EP - 871

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

Stability and bifurcation in plant-pathogens interactions

Abstract

Keywords

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