On the influence of cross-diffusion in pattern formation
Abstract
In this paper we consider the Shigesada-Kawasaki-Teramoto (SKT) model to account for stable inhomogeneous steady states exhibiting spatial segregation, which describe a situation of coexistence of two competing species. We provide a deeper understanding on the conditions required on both the cross-diffusion and the reaction coefficients for non-homogeneous steady states to exist, by combining a detailed linearized analysis with advanced numerical bifurcation methods via the continuation software pde2path. We report some numerical experiments suggesting that, when cross-diffusion is taken into account, there exist positive and stable non-homogeneous steady states outside of the range of parameters for which the coexistence homogeneous steady state is positive. Furthermore, we also analyze the case in which self-diffusion terms are considered.
Cite
@article{arxiv.1910.03436,
title = {On the influence of cross-diffusion in pattern formation},
author = {Maxime Breden and Christian Kuehn and Cinzia Soresina},
journal= {arXiv preprint arXiv:1910.03436},
year = {2019}
}