Normal forms for retarded functional differential equations with parameters and applications to Hopf bifurcation
type: Item
instance of: scholarly article
title: Normal forms for retarded functional differential equations with parameters and applications to Hopf bifurcation
zbMATH Open document ID: 0836.34068
author: Teresa Faria
author: Luis T. Magalhães
published in: Journal of Differential Equations
publication date: 1995-12-05T00:00:00Z
review text: From authors' abstract: ``The paper addresses, for retarded functional differential equations (FDEs) with parameters, the computation of normal forms associated with the flow on a finite-dimensional invariant manifold tangent to an invariant space for the infinitesimal generator of the linearized equation at a singularity. The analysis is based on the theory previously developed for FDEs without parameters by considering an extension of a phase space appropriate to the computation of these normal forms. As an application, the generic Hopf bifurcation for scalar retarded FDEs is considered''.
Mathematics Subject Classification ID: 34K05
Mathematics Subject Classification ID: 34C20
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 823546
zbMATH Keywords: retarded functional differential equations
zbMATH Keywords: normal forms
zbMATH Keywords: invariant manifold
zbMATH Keywords: Hopf bifurcation
reviewed by: Waldyr Muniz Oliva
MaRDI profile type: Publication
full work available at URL: jdeq.1995.1144
OpenAlex ID: W2009433941
DOI: 10.1006/JDEQ.1995.1144
description: scientific article; zbMATH DE number 823546