The accumulation of eigenvalues in a stability problem
type: Item
instance of: scholarly article
title: The accumulation of eigenvalues in a stability problem
zbMATH Open document ID: 0969.35079
DOI: 10.1016/S0167-2789(00)00061-0
author: Shunsaku Nii
published in: Physica D
publication date: 2000-07-11T00:00:00Z
review text: Sufficient criteria for instability of pulses in reaction-diffusion systems, formed by gluing together a front and a back at a PDE-unstable equilibrium, are given. The pulses exhibit a long intermediate plateau between front and back. In the travelling-wave ODE, the pulses are created as homoclinic orbits in a codimension-two heteroclinic loop bifurcation, sometimes referred to as a \(T\)-point. The PDE-instability is caused by an absolute instability of the unstable state at the plateau. As the length of the plateau tends to infinity, infinitely many unstable eigenvalues are shown to accumulate at a certain spectral value in the unstable complex plain.
reviewed by: Arnd Scheel
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 34C37
zbMATH DE Number: 1474681
zbMATH Keywords: sufficient criteria for instability of pulses
zbMATH Keywords: homoclinic orbits in a codimension-two heteroclinic loop bifurcation
MaRDI profile type: Publication
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full work available at URL: s0167-2789(00)00061-0
OpenAlex ID: W2162087888
description: scientific article; zbMATH DE number 1474681