Nonlocal boundary dynamics of traveling spots in a reaction-diffusion system |
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Authors: | Pismen L M |
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Affiliation: | Department of Chemical Engineering and Minerva Center for Nonlinear Physics of Complex Systems, Technion-Israel Institute of Technology, 32000 Haifa, Israel. |
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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. |
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