Difference resonances in a controlled van der Pol-Duffing oscillator involving time delay

Ji, JC; Zhang, N; Gao, W

Difference resonances in a controlled van der Pol-Duffing oscillator involving time delay

Ji, JC

Zhang, N

Gao, W

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Publication Type:: Journal Article
Citation:: Chaos, Solitons and Fractals, 2009, 42 (2), pp. 975 - 980
Issue Date:: 2009-10-30

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Field	Value	Language
dc.contributor.author	Ji, JC https://orcid.org/0000-0003-3280-5463	en_US
dc.contributor.author	Zhang, N https://orcid.org/0000-0001-6408-0044	en_US
dc.contributor.author	Gao, W	en_US
dc.date.issued	2009-10-30	en_US
dc.identifier.citation	Chaos, Solitons and Fractals, 2009, 42 (2), pp. 975 - 980	en_US
dc.identifier.issn	0960-0779	en_US
dc.identifier.uri	http://hdl.handle.net/10453/9386
dc.description.abstract	A non-resonant interaction of two Hopf bifurcations may appear after the trivial solution of a controlled van der Pol-Duffing oscillator without external excitation loses its stability, when two critical time delays corresponding to two Hopf bifurcations have the same value. In the vicinity of the non-resonant Hopf bifurcations, the presence of a periodic excitation in the controlled oscillator can induce difference resonances in the forced response, when the forcing frequency and the frequencies of the two Hopf bifurcations satisfy certain relationships. It is found that the frequency response curves of the controlled system under difference resonances are an isolated closed curve. The difference resonance response may admit two stable motions on a three-dimensional torus consisting of three frequencies. Illustrative examples are given to show the quasi-periodic motions. © 2009 Elsevier Ltd. All rights reserved.	en_US
dc.relation.ispartof	Chaos, Solitons and Fractals	en_US
dc.relation.isbasedon	10.1016/j.chaos.2009.02.029	en_US
dc.subject.classification	Mathematical Physics	en_US
dc.title	Difference resonances in a controlled van der Pol-Duffing oscillator involving time delay	en_US
dc.type	Journal Article
utslib.citation.volume	2	en_US
utslib.citation.volume	42	en_US
utslib.for	0102 Applied Mathematics	en_US
utslib.for	01 Mathematical Sciences	en_US
utslib.for	08 Information and Computing Sciences	en_US
utslib.for	09 Engineering	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Mechanical and Mechatronic Engineering
utslib.copyright.status	open_access
pubs.issue	2	en_US
pubs.publication-status	Published	en_US
pubs.volume	42	en_US

Abstract:

A non-resonant interaction of two Hopf bifurcations may appear after the trivial solution of a controlled van der Pol-Duffing oscillator without external excitation loses its stability, when two critical time delays corresponding to two Hopf bifurcations have the same value. In the vicinity of the non-resonant Hopf bifurcations, the presence of a periodic excitation in the controlled oscillator can induce difference resonances in the forced response, when the forcing frequency and the frequencies of the two Hopf bifurcations satisfy certain relationships. It is found that the frequency response curves of the controlled system under difference resonances are an isolated closed curve. The difference resonance response may admit two stable motions on a three-dimensional torus consisting of three frequencies. Illustrative examples are given to show the quasi-periodic motions. © 2009 Elsevier Ltd. All rights reserved.

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http://hdl.handle.net/10453/9386