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Stability and bifurcation in plant–pathogens interactions

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  • Buonomo, Bruno
  • Cerasuolo, Marianna

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.

Suggested Citation

  • Buonomo, Bruno & Cerasuolo, Marianna, 2014. "Stability and bifurcation in plant–pathogens interactions," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 858-871.
    • Handle: RePEc:eee:apmaco:v:232:y:2014:i:c:p:858-871
    DOI: 10.1016/j.amc.2014.01.127
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    References listed on IDEAS

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    1. Li, Guihua & Wang, Wendi & Jin, Zhen, 2006. "Global stability of an SEIR epidemic model with constant immigration," Chaos, Solitons & Fractals, Elsevier, vol. 30(4), pages 1012-1019.
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    Cited by:

    1. Pfab, Ferdinand & Diekmann, Odo & Bhattacharya, Souvik & Pugliese, Andrea, 2017. "Multiple coexistence equilibria in a two parasitoid-one host model," Theoretical Population Biology, Elsevier, vol. 113(C), pages 34-46.

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