GENERAL-THEORY OF INSTABILITIES FOR PATTERNS WITH SHARP INTERFACES INREACTION-DIFFUSION SYSTEMS

Citation
Cb. Muratov et Vv. Osipov, GENERAL-THEORY OF INSTABILITIES FOR PATTERNS WITH SHARP INTERFACES INREACTION-DIFFUSION SYSTEMS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 53(4), 1996, pp. 3101-3116
Citations number
47
Categorie Soggetti
Physycs, Mathematical","Phsycs, Fluid & Plasmas
ISSN journal
1063651X
Volume
53
Issue
4
Year of publication
1996
Part
A
Pages
3101 - 3116
Database
ISI
SICI code
1063-651X(1996)53:4<3101:GOIFPW>2.0.ZU;2-8
Abstract
An asymptotic method for finding instabilities of arbitrary d-dimensio nal large-amplitude patterns in a wide class of reaction-diffusion sys tems is presented. The complete stability analysis of two- and three-d imensional localized patterns is carried out. It is shown that in the considered class of systems the criteria for different types of instab ilities are universal. The specific nonlinearities enter the criteria only via three numerical constants of order 1. The analysis performed explains the self-organization scenarios observed in the recent experi ments and numerical simulations of some concrete reaction-diffusion sy stems.