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Forward-Time and Backward-Time Isochrons and Their Interactions.
- Source :
- SIAM Journal on Applied Dynamical Systems; 2015, Vol. 14 Issue 3, p1418-1453, 36p
- Publication Year :
- 2015
-
Abstract
- We consider isochrons of a periodic orbit in the planar FitzHugh-Nagumo system, that is, the curves of points that converge to the periodic orbit in phase with each other, and we extend this notion to isochrons of a focus equilibrium. We introduce the notion of backward-time isochrons, which are isochrons of the reversed-time system, and show that a cubic tangency occurs between a set of forward-time and backward-time isochrons. We call this moment of tangency a cubic isochron foliation tangency (CIFT). This phenomenon is not a local feature but happens globally throughout the annulus where both sets of isochrons coexist. We construct and discuss examples for three mechanisms for a CIFT: a global time-scale separation; a perturbation that increases the velocity along trajectories in a local region of phase space; and a canard explosion (in the Van der Pol system). [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 15360040
- Volume :
- 14
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- SIAM Journal on Applied Dynamical Systems
- Publication Type :
- Academic Journal
- Accession number :
- 117047745
- Full Text :
- https://doi.org/10.1137/15M1010191