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

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.