Nonlocal Boundary Dynamics of Traveling Spots in a Reaction-Diffusion System
- 15 January 2001
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 86 (3), 548-551
- https://doi.org/10.1103/physrevlett.86.548
Abstract
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.Keywords
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