AffiliationUniv Arizona, Dept Math, Tucson, AZ 85721 USA
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CitationSIAM J. APPLIED DYNAMICAL SYSTEMS Vol. 17, No. 1, pp. 236–349
Rights© 2018 Society for Industrial and Applied Mathematics
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AbstractThe FitzHugh Nagumo equations are known to admit fast traveling pulse solutions with monotone tails. It is also known that this system admits traveling pulses with exponentially decaying oscillatory tails. Upon numerical continuation in parameter space, it has been observed that the oscillations in the tails of the pulses grow into a secondary excursion resembling a second copy of the primary pulse. In this paper, we outline in detail the geometric mechanism responsible for this single-to-double-pulse transition, and we construct the transition analytically using geometric singular perturbation theory and blow-up techniques.
VersionFinal published version
SponsorsNSF [DMS-1148284, DMS-1408742]