Double Hopf bifurcation with strong resonances in delayed systems with nonlinearities
type: Item
instance of: scholarly article
title: Double Hopf bifurcation with strong resonances in delayed systems with nonlinearities
zbMATH Open document ID: 1190.37059
DOI: 10.1155/2009/759363
author: Jian Xu
author: Kwok-wai Chung
published in: Mathematical Problems in Engineering
publication date: 2010-04-23T00:00:00Z
full work available at URL: https://eudml.org/doc/232140
review text: Summary: An efficient method is proposed to study delay-induced strong resonant double Hopf bifurcation for nonlinear systems with time delay. As an illustration, the proposed method is employed to investigate the \(1 : 2\) double Hopf bifurcation in the van der Pol system with time delay. Dynamics arising from the bifurcation are classified qualitatively and expressed approximately in a closed form for either square or cubic nonlinearity. The results show that \(1 : 2\) resonance can lead to codimension-three and codimension-two bifurcations. The validity of analytical predictions is shown by their consistency with numerical simulations.
Mathematics Subject Classification ID: 37G10
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 5700461
Wikidata QID: Q58649486
MaRDI profile type: Publication
OpenAlex ID: W2141901926
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description: scientific article; zbMATH DE number 5700461