Two simple criterion to prove the existence of patterns in reaction-diffusion models of two components
Analysis of PDEs
2023-12-19 v1
Abstract
The aim of this work is to study the effect of diffusion on the stability of the equilibria in a general two-components reaction-diffusion system with Neumann boundary conditions in the space of continuous functions. As by product, we establish sufficient conditions on the diffusive coefficients and other parameters for such a reaction-diffusion model to exhibit patterns and we analyze their stability. We apply the results obtained in this paper to explore under which parameters values a Turing bifurcation can occur, given rise to non uniform stationary solutions (patterns) for a reaction-diffusion predator-prey model with variable mortality and Hollyn's type II functional response.
Keywords
Cite
@article{arxiv.2312.10231,
title = {Two simple criterion to prove the existence of patterns in reaction-diffusion models of two components},
author = {Francisco J. Vielma-Leal and Miguel A. D. R. Palma and Miguel Montenegro-Concha},
journal= {arXiv preprint arXiv:2312.10231},
year = {2023}
}
Comments
31 pages, 12 figures