Abstract:
This talk concerns the spatial dynamics approach to dynamical phenomena in partial differential equations (PDE) posed on the real line. 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.
This is joint work with Paul Carter (Minneapolis) and Bjorn Sandstede (Providence)
Due to some technical errors, the video of the talk is unavailable.