Jens Rademacher: Pulse replication and accumulation of eigenvalues

Submitted by Jorge Cisneros on

Speaker: Jens Rademacher, Universität Bremen

Date: February 11, 2021

Title: Pulse replication and accumulation of eigenvalues

Abstract: Motivated by pulse-replication phenomena observed in the FitzHugh-Nagumo equation, traveling pulses whose slow-fast profiles exhibit canard-like transitions are investigated. It is shown 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. The results are formulated for general systems that admit an appropriate slow-fast structure. This is joint work with Paul Carter (Minneapolis) and Bjorn Sandstede (Providence).