Pulse Replication and Accumulation of Eigenvalues
Abstract
Motivated by pulse-replication phenomena observed in the FitzHugh--Nagumo equation, we investigate traveling pulses whose slow/fast profiles exhibit canard-like transitions. We show that the spectra of the PDE linearization about such pulses may contain many point eigenvalues that accumulate onto a union of curves as the slow scale parameter approaches zero. The limit sets are related to the absolute spectrum of the homogeneous rest states involved in the canard-like transitions. Our results are formulated for general systems that admit an appropriate slow/fast structure.
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Information & Authors
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Published In
SIAM Journal on Mathematical Analysis
Pages: 3520 - 3576
DOI: 10.1137/20M1340113
ISSN (online): 1095-7154
Copyright
© 2021, Society for Industrial and Applied Mathematics.
History
Submitted: 26 May 2020
Accepted: 26 April 2021
Published online: 21 June 2021
Keywords
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Funding Information
Deutsche Forschungsgemeinschaft https://doi.org/10.13039/501100001659 : RA 2788/1-1
Funding Information
National Science Foundation https://doi.org/10.13039/100000001 : DMS-1714429
Funding Information
National Science Foundation https://doi.org/10.13039/100000001 : DMS-2016216
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