Electron. J. Differential Equations, Vol. 2026 (2026), No. 82, pp. 1-19.

Nonlocal mechanisms leading to instability in dry-land vegetation models

Gonzalo Galiano, Julian Velasco

Abstract:
We consider a system of partial differential equations arising in vegetation dynamics. Roots interactions are modeled through nonlocal reaction terms which, in the limit of negligible roots extension, collapse to local reaction terms. We study, by means of linear stability analysis and computational simulation, the emergence of pattern formation due to both Turing instability and nonlocal effects. We show that, in the physical reasonable parameter range, interchangeability of local and nonlocal models is not justified, since their corresponding patterns differ substantially.

Submitted June 11, 2026. Published October 19, 2026.
Math Subject Classifications: 45K05, 35K55, 35R09, 92D25, 35B35, 92C15.
Key Words: Nonlocal reaction; reaction-diffusion; stability; pattern formation; vegetation models.
DOI: 10.58997/ejde.2026.82

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Gonzalo Galiano
Department of Mathematics
University of Oviedo
Oviedo, Spain
email: galiano@uniovi.es
Julián Velasco
Department of Mathematics
University of Oviedo
Oviedo, Spain
email: julian@uniovi.es

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