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Title: Existence and stability analysis of spiky solutions for the Gierer-Meinhardt system with large reaction rates
Authors: Winter, M
Kolokolnikov, T
Wei, J
Keywords: Stability;Multiple-peaked solutions;Singular perturbations;Turing instability
Issue Date: 2009
Publisher: Elsevier
Citation: Physica D: Nonlinear Phenomena. 238(16): 1695-1710
Abstract: We study the Gierer-Meinhardt system in one dimension in the limit of large reaction rates. First we construct three types of solutions: (i) an interior spike; (ii) a boundary spike and (iii) two boundary spikes. Second we prove results on their stability. It is found that an interior spike is always unstable; a boundary spike is always stable. The two boundary spike configuration can be either stable or unstable, depending on the parameters. We fully classify the stability in this case. We characterise the destabilizing eigenfunctions in all cases. Numerical simulations are shown which are in full agreement with the analytical results.
ISSN: 0167-2789
Appears in Collections:Dept of Mathematics Research Papers
Mathematical Sciences

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