Nonlocal Boundary Dynamics of Traveling Spots in a Reaction-Diffusion System
arXiv:nlin/0005049 · doi:10.1103/PhysRevLett.86.548
Abstract
The boundary integral method is extended to derive closed integro-differential equations 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, so that propagating spots can be stabilized without introducing additional long-range variables.
RevTeX 4 pages, 1 figure
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