Hopf bifurcation and stability of periodic solutions for van der Pol equation with time delay
type: Item
instance of: scholarly article
title: Hopf bifurcation and stability of periodic solutions for van der Pol equation with time delay
zbMATH Open document ID: 1138.34348
author: Wenwu Yu
author: Jinde Cao
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2005-06-27T00:00:00Z
review text: Consider the van der Pol equation with delay \[ \dot x(t)= y(t-\tau)- ax(t-\tau)- b(x(t- \tau))^2, \] \[ \dot y(t)=- x(t-\tau). \] The authors study Hopf bifurcation of the origin with \(\tau\) as bifurcation parameter in dependence on the parameter \(a\). By means of a center manifold and a normal form they determine the bifurcation direction and the stability of the bifurcating periodic solution.
reviewed by: Klaus R. Schneider
Mathematics Subject Classification ID: 34K18
Mathematics Subject Classification ID: 34K19
Mathematics Subject Classification ID: 34K17
Mathematics Subject Classification ID: 34K20
zbMATH DE Number: 2183190
zbMATH Keywords: Van der Pol equation
zbMATH Keywords: Time delay
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: Periodic solutions
MaRDI profile type: Publication
full work available at URL: j.na.2005.03.017
OpenAlex ID: W2096565917
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DOI: 10.1016/J.NA.2005.03.017
description: scientific article; zbMATH DE number 2183190