Equivariant Hopf bifurcation for functional differential equations of mixed type
type: Item
instance of: scholarly article
title: Equivariant Hopf bifurcation for functional differential equations of mixed type
zbMATH Open document ID: 1263.34100
author: Shangjiang Guo
published in: Applied Mathematics Letters
publication date: 2011-03-10T00:00:00Z
review text: The paper proves the equivariant Hopf bifurcation theorem for functional-differential equations of mixed type (that is, equations, for example, of the form \(\dot x(t)=f(x(t),x(t-\tau_1),x(t+\tau_2))\) with \(\tau_1\), \(\tau_2>0\)) with symmetry. By resorting to Lyapunov-Schmidt reduction techniques on spaces of periodic functions, the paper avoids all difficulties associated with mixed-type equations (on the space of periodic functions future and past are indistinguishable). In fact, the results and arguments in the paper are identical to the case containing only delays, for example, considered by \textit{S. Gou} and \textit{L. Huang} [Physica D 183, No. 1--2, 19--44 (2003; Zbl 1041.68079)].
reviewed by: Jan Sieber
Mathematics Subject Classification ID: 34K18
Mathematics Subject Classification ID: 34C14
zbMATH DE Number: 5864286
zbMATH Keywords: Lyapunov-Schmidt reduction
zbMATH Keywords: equivariant Hopf bifurcation
zbMATH Keywords: functional differential equations of mixed type
zbMATH Keywords: Lie group
MaRDI profile type: Publication
full work available at URL: j.aml.2010.12.017
OpenAlex ID: W2014344946
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DOI: 10.1016/J.AML.2010.12.017
description: scientific article; zbMATH DE number 5864286