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
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.