Constructing far-from-equilibrium patterns in a cross-diffusion vegetation-autotoxicity model

arXiv (Cornell University)

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.

Authors 3

1. Annalisa Iuorio

   Parthenope University of Naples

   Affiliation as printed

   Department of Engineering , Parthenope University of Naples

2. Cinzia Soresina

   University of Trento

   Affiliation as printed

   Department of Mathematics , University of Trento

3. Frits Veerman Aachen Mathematical Institute

   Leiden University

   Affiliation as printed

   Mathematical Institute , University of Leiden