English

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