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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Vilnius University Press
2017-09-01
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Online Access: | http://www.zurnalai.vu.lt/nonlinear-analysis/article/view/13368 |
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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.
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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 |