Pulse replication and accumulation of eigenvalues

24 May 2020  ·  Paul Carter, Jens D. M. Rademacher, Björn Sandstede ·

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. read more

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Pattern Formation and Solitons Analysis of PDEs Dynamical Systems 35B35, 35P15, 35C07, 35B25, 34E17, 37L15