Minimum nonlinearity for pattern-forming Turing instability in a mathematical autocatalytic model
Pattern Formation and Solitons
2024-12-19 v1 Mathematical Physics
Dynamical Systems
math.MP
Abstract
Pattern formation is ubiquitous in nature and the mechanism widely-accepted to underlay them is based on the Turing instability, predicted by Alan Turing decades ago. This is a non-trivial mechanism that involves nonlinear interaction terms between the different species involved and transport mechanisms. We present here a mathematical analysis aiming to explore the mathematical constraints that a reaction-diffusion dynamical model should comply in order to exhibit a Turing instability. The main conclusion limits the existence of this instability to nonlinearity degrees larger or equal to three.
Cite
@article{arxiv.2412.13783,
title = {Minimum nonlinearity for pattern-forming Turing instability in a mathematical autocatalytic model},
author = {Javier López-Pedrares and Marcos Suárez-Vázquez and Juan Pérez-Mercader and Alberto P. Muñuzuri},
journal= {arXiv preprint arXiv:2412.13783},
year = {2024}
}