Bifurcations of periodic solutions of delay differential equations
type: Item
instance of: scholarly article
title: Bifurcations of periodic solutions of delay differential equations
zbMATH Open document ID: 1027.34081
DOI: 10.1016/S0022-0396(02)00106-7
published in: Journal of Differential Equations
publication date: 2003-05-25T00:00:00Z
review text: The author extends the method of \textit{J. L. Kaplan} and \textit{J. A. Yorke} [J. Differ. Equations 23, 293-314 (1977; Zbl 0307.34070)] to prove the existence of periodic solutions with certain period in scalar delay differential equations of the type \(\dot x(t)= F(x(t), x(t-r), x(t-2r))\), where \(F\) satisfies the relation \(F(x,y,-x)=-F(-x,-y,x)\). For \(F\) depending on parameters, the paper gives conditions under which Hopf and saddle-node bifurcations of periodic solutions occur. Moreover, the author provides examples showing that Hopf and saddle-node bifurcations often occur infinitely many times.
reviewed by: Jan Sieber
Mathematics Subject Classification ID: 34K18
Mathematics Subject Classification ID: 34K13
zbMATH DE Number: 1915519
zbMATH Keywords: delay differential equation
zbMATH Keywords: periodic solution
zbMATH Keywords: bifurcation
author: Maoan Han
MaRDI profile type: Publication
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full work available at URL: s0022-0396(02)00106-7
OpenAlex ID: W2005946114
description: scientific article; zbMATH DE number 1915519