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    Unpeeling a Homoclinic Banana in the FitzHugh--Nagumo System

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    Author
    Carter, Paul
    Sandstede, Björn
    Affiliation
    Univ Arizona, Dept Math, Tucson, AZ 85721 USA
    Issue Date
    2018
    Keywords
    geometric singular perturbation theory
    blow-up
    FitzHugh Nagumo
    traveling waves
    canards
    
    Metadata
    Show full item record
    Publisher
    SIAM PUBLICATIONS
    Citation
    SIAM J. APPLIED DYNAMICAL SYSTEMS Vol. 17, No. 1, pp. 236–349
    Journal
    SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
    Rights
    © 2018 Society for Industrial and Applied Mathematics.
    Collection Information
    This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.
    Abstract
    The 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.
    Note
    No embargo.
    ISSN
    1536-0040
    DOI
    10.1137/16M1080707
    Version
    Final published version
    Sponsors
    NSF [DMS-1148284, DMS-1408742]
    Additional Links
    https://epubs.siam.org/doi/10.1137/16M1080707
    ae974a485f413a2113503eed53cd6c53
    10.1137/16M1080707
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