Turing instabilities for three interacting species
Abstract
In this paper, I prove necessary and sufficient conditions for the existence of Turing instabilities in a general system with three interacting species. Turing instabilities describe situations when a stable steady state of a reaction system (ordinary differential equation) becomes an unstable homogeneous steady state of the corresponding reaction-diffusion system (partial differential equation). Similarly to a well-known inequality condition for Turing instabilities in a system with two species, I find a set of inequality conditions for a system with three species. Furthermore, I distinguish conditions for the Turing instability when spatial perturbations grow steadily and the Turing-Hopf instability when spatial perturbations grow and oscillate in time simultaneously.
Cite
@article{arxiv.2405.14682,
title = {Turing instabilities for three interacting species},
author = {Vit Piskovsky},
journal= {arXiv preprint arXiv:2405.14682},
year = {2024}
}
Comments
6 pages, 1 figure