Turing Instability in a Boundary-fed System
Abstract
The formation of localized structures in the chlorine dioxide-idodine-malonic acid (CDIMA) reaction-diffusion system is investigated numerically using a realistic model of this system. We analyze the one-dimensional patterns formed along the gradients imposed by boundary feeds, and study their linear stability to symmetry-breaking perturbations (Turing instability) in the plane transverse to these gradients. We establish that an often-invoked simple local linear analysis which neglects longitudinal diffusion is inappropriate for predicting the linear stability of these patterns. Using a fully nonuniform analysis, we investigate the structure of the patterns formed along the gradients and their stability to transverse Turing pattern formation as a function of the values of two control parameters: the malonic acid feed concentration and the size of the reactor in the dimension along the gradients. The results from this investigation are compared with existing experiments.
Cite
@article{arxiv.patt-sol/9806006,
title = {Turing Instability in a Boundary-fed System},
author = {S. Setayeshgar and M. C. Cross},
journal= {arXiv preprint arXiv:patt-sol/9806006},
year = {2009}
}
Comments
41 pages, 18 figures, to be published in Physical Review E