Nonlocal boundary dynamics of traveling spots in a reaction-diffusion system.
The boundary integral method is extended to derive a closed integro-differential equation applicable to computation of the shape and propagation speed of a steadily moving spot and to the analysis of dynamic instabilities in the sharp boundary limit. Expansion of the boundary integral near the locus of traveling instability in a standard reaction-diffusion model proves that the bifurcation is supercritical whenever the spot is stable to splitting. Thus, stable propagating spots do already exist in the basic activator-inhibitor model, without additional long-range variables.
Pismen
L M
LM
Department of Chemical Engineering and Minerva Center for Nonlinear Physics of Complex Systems, Technion-Israel Institute of Technology, 32000 Haifa, Israel.