Nonlocal Boundary Dynamics of Traveling Spots in a Reaction-Diffusion System
Pattern Formation and Solitons
2016-09-07 v1
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.
Keywords
Cite
@article{arxiv.nlin/0005049,
title = {Nonlocal Boundary Dynamics of Traveling Spots in a Reaction-Diffusion System},
author = {L. M. Pismen},
journal= {arXiv preprint arXiv:nlin/0005049},
year = {2016}
}
Comments
RevTeX 4 pages, 1 figure