Affiliation
Univ Arizona, Dept Math, Tucson, AZ 85721 USAIssue Date
2018
Metadata
Show full item recordPublisher
SIAM PUBLICATIONSCitation
SIAM J. APPLIED DYNAMICAL SYSTEMS Vol. 17, No. 1, pp. 236–349Rights
© 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
1536-0040Version
Final published versionSponsors
NSF [DMS-1148284, DMS-1408742]Additional Links
https://epubs.siam.org/doi/10.1137/16M1080707ae974a485f413a2113503eed53cd6c53
10.1137/16M1080707