Nonresonant Hopf-Hopf bifurcation and a chaotic attractor in neutral functional differential equations
type: Item
instance of: scholarly article
title: Nonresonant Hopf-Hopf bifurcation and a chaotic attractor in neutral functional differential equations
zbMATH Open document ID: 1315.34075
author: Ben Niu
author: Weihua Jiang
published in: Journal of Mathematical Analysis and Applications
publication date: 2012-12-04T00:00:00Z
full work available at URL: https://arxiv.org/abs/1402.0287
review text: A framework for the occurrence of the nonresonant Hopf-Hopf bifurcation in an NFDE with parameters is established. The normal form up to the third order is obtained. Then the framework is applied to a Van der Pols equation with extended delayed feedback. Hopf-Hopf points are identified and the normal forms are calculated. A bifurcation diagram is derived to see that a rich dynamics such as periodic solutions, quasi-periodic solutions, even chaos may occur as the parameter values fall in the corresponding parameter regions.
reviewed by: Liancheng Wang
Mathematics Subject Classification ID: 34K18
Mathematics Subject Classification ID: 34K40
Mathematics Subject Classification ID: 34K17
Mathematics Subject Classification ID: 34K13
Mathematics Subject Classification ID: 34K23
zbMATH DE Number: 6112319
zbMATH Keywords: neutral functional differential equations
zbMATH Keywords: nonresonant Hopf-Hopf bifurcation
zbMATH Keywords: van der Pol's equations
zbMATH Keywords: quasi-periodic solutions
zbMATH Keywords: chaos
MaRDI profile type: Publication
OpenAlex ID: W1966282047
arXiv ID: 1402.0287
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DOI: 10.1016/J.JMAA.2012.08.051
description: scientific article