JournalsrlmVol. 25, No. 2pp. 191–216

Local versus nonlocal interactions in a reaction-diffusion system of population dynamics

  • Fabio Punzo

    Università degli Studi di Milano, Italy
  • Tetiana Savitska

    Università di Roma La Sapienza, Italy
Local versus nonlocal interactions in a reaction-diffusion system of population dynamics cover
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Abstract

We study existence of patterns for a reaction-diffusion system of population dynamics with nonlocal interaction. We address the system as a bifurcation problem (the bifurcation parameter being the diffusivity of one species), and investigate the possibility of patterns bifurcating out of a constant steady state solution via Turing destabilization. It is shown that the nonlocal character of the interaction enhances the possibility that patterns exist with respect to the case of the companion problem with local interaction.

Cite this article

Fabio Punzo, Tetiana Savitska, Local versus nonlocal interactions in a reaction-diffusion system of population dynamics. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 25 (2014), no. 2, pp. 191–216

DOI 10.4171/RLM/674