Open AccessLocal versus nonlocal interactions in a reaction-diffusion system of population dynamics
Author(s) -
Fabio Punzo,
Tetiana Savitska
Publication year - 2014
Publication title -
atti della accademia nazionale dei lincei. rendiconti lincei. matematica e applicazioni
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.824
H-Index - 28
eISSN - 1720-0768
pISSN - 1120-6330
DOI - 10.4171/rlm/674
Subject(s) - bifurcation , reaction–diffusion system , turing , statistical physics , population , constant (computer programming) , dynamics (music) , steady state (chemistry) , diffusion , character (mathematics) , thermal diffusivity , state (computer science) , physics , mathematics , classical mechanics , mathematical analysis , computer science , nonlinear system , thermodynamics , chemistry , geometry , quantum mechanics , demography , sociology , acoustics , algorithm , programming language
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