Pulse Replication and Accumulation of Eigenvalues
| Autor: | Paul A. Carter, Björn Sandstede, Jens D. M. Rademacher |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Quantitative Biology::Neurons and Cognition
Applied Mathematics 010102 general mathematics Mathematical analysis Spectral stability FOS: Physical sciences Pattern Formation and Solitons (nlin.PS) Dynamical Systems (math.DS) Nonlinear Sciences - Pattern Formation and Solitons 01 natural sciences 010305 fluids & plasmas Computational physics Pulse (physics) Computational Mathematics Mathematics - Analysis of PDEs 0103 physical sciences Replication (statistics) FOS: Mathematics Mathematics - Dynamical Systems 0101 mathematics 35B35 35P15 35C07 35B25 34E17 37L15 Analysis Eigenvalues and eigenvectors Analysis of PDEs (math.AP) Mathematics |
| Zdroj: | SIAM Journal on Mathematical Analysis. 53:3520-3576 |
| ISSN: | 1095-7154 0036-1410 |
| DOI: | 10.1137/20m1340113 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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