Hopf bifurcation calculations for functional differential equations
type: Item
instance of: scholarly article
title: Hopf bifurcation calculations for functional differential equations
zbMATH Open document ID: 0592.34048
DOI: 10.1016/0022-247X(85)90163-5
author: Harlan W. Stech
published in: Journal of Mathematical Analysis and Applications
publication date: 1985-01-01T00:00:00Z
review text: The author presents an alternate method for analyzing the Hopf bifurcation problem in a class of functional differential equations with unbounded delay: \(\dot y(t)=\int^{0}_{\infty}d\eta (\alpha;s)y_ t(s)+H(\alpha;y_ t).\) An advantage of this method over previous ones for example by \textit{S.-N. Chow} and \textit{J. Mallet-Paret} [J. Differ. Equations 26, 112-159 (1977; Zbl 0367.34033)] is that it avoids all reference to the infinite-dimensional nature of the problem. Its importance lies both in its generality and its relative ease of applications. The method is based on Lyapunov-Schmidt means and is motivated by the work of \textit{J. C. De Oliveira} and \textit{J. K. Hale} [Tôhoku Math. J., II. Ser. 32, 577-592 (1980; Zbl 0454.34035)].
Mathematics Subject Classification ID: 34K99
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 3951051
zbMATH Keywords: Hopf bifurcation problem
zbMATH Keywords: functional differential equations
zbMATH Keywords: unbounded delay
zbMATH Keywords: Lyapunov-Schmidt means
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3951051