English

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 dd-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.

Keywords

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)