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Title: On the Nonexistence of Terrestrial Canards: Linking Canards and Rivers
Award ID(s):
1951095
NSF-PAR ID:
10465241
Author(s) / Creator(s):
;
Date Published:
Journal Name:
SIAM Journal on Applied Dynamical Systems
Volume:
21
Issue:
4
ISSN:
1536-0040
Page Range / eLocation ID:
2432 to 2462
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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  1. A class of two-fast, one-slow multiple timescale dynamical systems is considered that contains the system of ordinary differential equations obtained from seeking travelling-wave solutions to the FitzHugh-Nagumo equations in one space dimension. The question addressed is the mechanism by which a small-amplitude periodic orbit, created in a Hopf bifurcation, undergoes rapid amplitude growth in a small parameter interval, akin to a canard explosion. The presence of a saddle-focus structure around the slow manifold implies that a single periodic orbit undergoes a sequence of folds as the amplitude grows. An analysis is performed under some general hypotheses using a combination ideas from the theory of canard explosion and Shilnikov analysis. An asymptotic formula is obtained for the dependence of the parameter location of the folds on the singular parameter and parameters that control the saddle focus eigenvalues. The analysis is shown to agree with numerical results both for a synthetic normal-form example and the FitzHugh-Nagumo system.

     
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