Hopf-pitchfork bifurcation of coupled van der Pol oscillator with delay

In this paper, the Hopf-pitchfork bifurcation of coupled van der Pol with delay is studied. The interaction coefficient and time delay are taken as two bifurcation parameters. Firstly, the normal form is gotten by performing a center manifold reduction and using the normal form theory developed by...

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Main Authors:	Yuting Cai, Chunrui Zhang
Format:	Article
Language:	English
Published:	Vilnius University Press 2017-09-01
Series:	Nonlinear Analysis
Subjects:	delay Hopf-pitchfork bifurcation stability coupled van der Pol model normal form
Online Access:	http://www.zurnalai.vu.lt/nonlinear-analysis/article/view/13368

id	doaj-a077e0cb3b914ec99fa80c60881fbc11
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spelling	doaj-a077e0cb3b914ec99fa80c60881fbc112020-11-25T00:41:14ZengVilnius University PressNonlinear Analysis1392-51132335-89632017-09-0122510.15388/NA.2017.5.2Hopf-pitchfork bifurcation of coupled van der Pol oscillator with delayYuting Cai0Chunrui Zhang1Northeast Forestry University, ChinaNortheast Forestry University, China In this paper, the Hopf-pitchfork bifurcation of coupled van der Pol with delay is studied. The interaction coefficient and time delay are taken as two bifurcation parameters. Firstly, the normal form is gotten by performing a center manifold reduction and using the normal form theory developed by Faria and Magalhães. Secondly, bifurcation diagrams and phase portraits are given through analyzing the unfolding structure. Finally, numerical simulations are used to support theoretical analysis. http://www.zurnalai.vu.lt/nonlinear-analysis/article/view/13368delayHopf-pitchfork bifurcationstabilitycoupled van der Pol modelnormal form
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Yuting Cai Chunrui Zhang
spellingShingle	Yuting Cai Chunrui Zhang Hopf-pitchfork bifurcation of coupled van der Pol oscillator with delay Nonlinear Analysis delay Hopf-pitchfork bifurcation stability coupled van der Pol model normal form
author_facet	Yuting Cai Chunrui Zhang
author_sort	Yuting Cai
title	Hopf-pitchfork bifurcation of coupled van der Pol oscillator with delay
title_short	Hopf-pitchfork bifurcation of coupled van der Pol oscillator with delay
title_full	Hopf-pitchfork bifurcation of coupled van der Pol oscillator with delay
title_fullStr	Hopf-pitchfork bifurcation of coupled van der Pol oscillator with delay
title_full_unstemmed	Hopf-pitchfork bifurcation of coupled van der Pol oscillator with delay
title_sort	hopf-pitchfork bifurcation of coupled van der pol oscillator with delay
publisher	Vilnius University Press
series	Nonlinear Analysis
issn	1392-5113 2335-8963
publishDate	2017-09-01
description	In this paper, the Hopf-pitchfork bifurcation of coupled van der Pol with delay is studied. The interaction coefficient and time delay are taken as two bifurcation parameters. Firstly, the normal form is gotten by performing a center manifold reduction and using the normal form theory developed by Faria and Magalhães. Secondly, bifurcation diagrams and phase portraits are given through analyzing the unfolding structure. Finally, numerical simulations are used to support theoretical analysis.
topic	delay Hopf-pitchfork bifurcation stability coupled van der Pol model normal form
url	http://www.zurnalai.vu.lt/nonlinear-analysis/article/view/13368
work_keys_str_mv	AT yutingcai hopfpitchforkbifurcationofcoupledvanderpoloscillatorwithdelay AT chunruizhang hopfpitchforkbifurcationofcoupledvanderpoloscillatorwithdelay
_version_	1725286447709159424

Hopf-pitchfork bifurcation of coupled van der Pol oscillator with delay

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