Pulse replication and accumulation of eigenvalues
Pattern Formation and Solitons
2021-02-15 v2 Analysis of PDEs
Dynamical Systems
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.
Cite
@article{arxiv.2005.11683,
title = {Pulse replication and accumulation of eigenvalues},
author = {Paul Carter and Jens D. M. Rademacher and Björn Sandstede},
journal= {arXiv preprint arXiv:2005.11683},
year = {2021}
}