On the stability bifurcation of a nonlinear time delay system
type: Item
instance of: scholarly article
title: On the stability bifurcation of a nonlinear time delay system
zbMATH Open document ID: 0907.34054
DOI: 10.1016/S0005-1098(97)00208-2
author: M. S. Fofana
author: David Lamb
published in: Automatica
publication date: 1998-10-27T00:00:00Z
review text: The authors consider the stability problem for nonlinear time delay systems. They use a center manifold approach in order to investigate the stability of trivial and nontrivial solutions to some equations studied earlier by \textit{J. Bentsman, K. S. Hong} and \textit{J. Fakhfakh} [Automatica 27, No. 3, 491-500 (1991; Zbl 0754.93065)]. The investigation of Hopf bifurcation of the nonlinear delay equation with fixed delay can be reduced to the study of a system of two ODEs. Explicit bifurcation equations are derived using a first approximation of the integral averaging method. Stability and instability regions are identified.
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34C29
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 1192894
zbMATH Keywords: nonlinear time delay systems
zbMATH Keywords: stability
zbMATH Keywords: bifurcation
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: averaging method
reviewed by: S. Yanchuk
MaRDI profile type: Publication
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full work available at URL: s0005-1098(97)00208-2
OpenAlex ID: W2073323270
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description: scientific article; zbMATH DE number 1192894