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Zip bifurcation in a competitive system with diffusion

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Abstract

We study the existence of a global attractor in a reaction-diffusion system which describes the interaction among n + 1 species, amongst which n species of predators compete for a single prey. Also, we prove the persistence of the zip bifurcation phenomenon for the reaction-diffusion system, which was introduced by Farkas [5] for a three dimensional ODE prey-predator system.

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Authors and Affiliations

  1. Instituto Universitário do Araguaia-Universidade Federal de Mato Grosso, Rod. MT-100km 3,5, Campus Universitário, CEP 78.698-000, Pontal do Araguaia, MT, Brazil

    Jocirei D. Ferreira

  2. Instituto de Matemática e Estatística, Universidade de São Paulo, Departamento de Matemática, Rua do Matão, 1010, Cidade Universitária, CEP 05508-090, São Paulo, SP, Brazil

    Luiz Augusto F. de Oliveira

Authors
  1. Jocirei D. Ferreira
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  2. Luiz Augusto F. de Oliveira
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Corresponding author

Correspondence to Luiz Augusto F. de Oliveira.

Additional information

This paper is dedicated to the memory of professor Miklós Farkas, colleague and friend.

Supported by CNPq — Conselho Nacional de Desenvolviemnto Científico e Tecnológico.

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Ferreira, J.D., de Oliveira, L.A.F. Zip bifurcation in a competitive system with diffusion. Differ Equ Dyn Syst 17, 37–53 (2009). https://doi.org/10.1007/s12591-009-0003-0

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