Hopf bifurcation at a double eigenvalue
type: Item
instance of: scholarly article
title: Hopf bifurcation at a double eigenvalue
zbMATH Open document ID: 0888.34030
author: Nguyen Xuan Tan
published in: Acta Mathematica Vietnamica
publication date: 1998-06-11T00:00:00Z
review text: Consider the \(n\)-dimensional system of ordinary differential equations \[ dx/dt= f(x,\mu)\tag{\(*\)} \] depending on a real parameter. \(f\) is assumed to be smooth and to satisfy \(f(0,\mu)\equiv 0\;\forall\mu\). Let be \(A(\mu):= f_x(0,\mu)\). The author studies Hopf bifurcation of \((*)\) in case that \(\pm i\) are double eigenvalues of \(A(\mu_0)\). The essential tool is the Lyapunov-Schmidt reduction technique. There is no comparison of the obtained results with other results concerning Hopf bifurcation at a multiple eigenvalue.
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 1083679
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: Lyapunov-Schmidt reduction
zbMATH Keywords: multiple eigenvalue
reviewed by: Klaus R. Schneider
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1083679