Institute for Mathematics and Its Applications
Moshe Sheintuch, Technion
We review recent results on pattern selection in the reaction-diffusion
one- or two-dimensional system
xt-Dx= f(x,y, l), yt= e g(x,y), subject to
(i) physical sources of such interactions and experimental observations in catalytic and electrochemical systems;
(ii) the main emerging patterns and their classification according to their symmetry;
(iii) the bifurcation between patterns;
(iv) approximate solutions based on front-motion and front-interaction, and
(v) patterns when f(x)=0 is tristable and can sustain several fronts.
The rich class of patterns simulated in a ribbon can be classified as stationary-front solutions (including oscillating fronts and antiphase oscillations) and moving pulse solutions (unidirectional, back-and-forth and source-points). Patterns on a disk may be classified as circular (including oscillatory or moving target patterns), rotating (stationary or moving spiral wave) and other patterns.