Constructing far-from-equilibrium patterns in a cross-diffusion vegetation-autotoxicity model
Dynamical Systems
2026-07-17 v1 Pattern Formation and Solitons
Abstract
Using geometric singular perturbation theory, we construct stationary, periodic, front-type far-from-equilibrium patterns in a cross-diffusion model for plant growth under the influence of toxicity. We show how existing techniques for the analysis of far-from-equilibrium patterns in one spatial dimension can be extended to include cross-diffusion terms and prove the existence of a one-parameter family of these patterns. For a general cross-diffusion model class, we show when front-type patterns may appear depending on the shape of the critical manifold, which is determined by the specific properties of the reaction terms.
Cite
@article{arxiv.2607.15692,
title = {Constructing far-from-equilibrium patterns in a cross-diffusion vegetation-autotoxicity model},
author = {Annalisa Iuorio and Cinzia Soresina and Frits Veerman},
journal= {arXiv preprint arXiv:2607.15692},
year = {2026}
}