General theory of instabilities for patterns with sharp interfaces in reaction-diffusion systems
patt-sol
2009-10-30 v1 Pattern Formation and Solitons
Abstract
An asymptotic method for finding instabilities of arbitrary -dimensional large-amplitude patterns in a wide class of reaction-diffusion systems is presented. The complete stability analysis of 2- and 3-dimensional localized patterns is carried out. It is shown that in the considered class of systems the criteria for different types of instabilities are universal. The specific nonlinearities enter the criteria only via three numerical constants of order one. The performed analysis explains the self-organization scenarios observed in the recent experiments and numerical simulations of some concrete reaction-diffusion systems.
Cite
@article{arxiv.patt-sol/9603001,
title = {General theory of instabilities for patterns with sharp interfaces in reaction-diffusion systems},
author = {C. B. Muratov and V. V. Osipov},
journal= {arXiv preprint arXiv:patt-sol/9603001},
year = {2009}
}
Comments
21 pages (RevTeX), 8 figures (Postscript). To appear in Phys. Rev. E (April 1st, 1996)