One-to-three resonant Hopf bifurcations of a maglev system

Zhang, L; Ji, JC

One-to-three resonant Hopf bifurcations of a maglev system

Zhang, L

Ji, JC

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Publication Type:: Journal Article
Citation:: Nonlinear Dynamics, 2018, 93 (3), pp. 1277 - 1286
Issue Date:: 2018-08-01

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Field	Value	Language
dc.contributor.author	Zhang, L https://orcid.org/0000-0002-8687-1186	en_US
dc.contributor.author	Ji, JC https://orcid.org/0000-0003-3280-5463	en_US
dc.date.issued	2018-08-01	en_US
dc.identifier.citation	Nonlinear Dynamics, 2018, 93 (3), pp. 1277 - 1286	en_US
dc.identifier.issn	0924-090X	en_US
dc.identifier.uri	http://hdl.handle.net/10453/132399
dc.description.abstract	© 2018, Springer Science+Business Media B.V., part of Springer Nature. This paper studies the dynamics of a maglev system around 1:3 resonant Hopf–Hopf bifurcations. When two pairs of purely imaginary roots exist for the corresponding characteristic equation, the maglev system has an interaction of Hopf–Hopf bifurcations at the intersection of two bifurcation curves in the feedback control parameter and time delay space. The method of multiple time scales is employed to drive the bifurcation equations for the maglev system by expressing complex amplitudes in a combined polar-Cartesian representation. The dynamics behavior in the vicinity of 1:3 resonant Hopf–Hopf bifurcations is studied in terms of the controller’s parameters (time delay and two feedback control gains). Finally, numerical simulations are presented to support the analytical results and demonstrate some interesting phenomena for the maglev system.	en_US
dc.relation.ispartof	Nonlinear Dynamics	en_US
dc.relation.isbasedon	10.1007/s11071-018-4258-2	en_US
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject.classification	Acoustics	en_US
dc.title	One-to-three resonant Hopf bifurcations of a maglev system	en_US
dc.type	Journal Article
utslib.citation.volume	3	en_US
utslib.citation.volume	93	en_US
utslib.for	0101 Pure Mathematics	en_US
utslib.for	01 Mathematical 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	closed_access	*
pubs.issue	3	en_US
pubs.publication-status	Published	en_US
pubs.volume	93	en_US

Abstract:

© 2018, Springer Science+Business Media B.V., part of Springer Nature. This paper studies the dynamics of a maglev system around 1:3 resonant Hopf–Hopf bifurcations. When two pairs of purely imaginary roots exist for the corresponding characteristic equation, the maglev system has an interaction of Hopf–Hopf bifurcations at the intersection of two bifurcation curves in the feedback control parameter and time delay space. The method of multiple time scales is employed to drive the bifurcation equations for the maglev system by expressing complex amplitudes in a combined polar-Cartesian representation. The dynamics behavior in the vicinity of 1:3 resonant Hopf–Hopf bifurcations is studied in terms of the controller’s parameters (time delay and two feedback control gains). Finally, numerical simulations are presented to support the analytical results and demonstrate some interesting phenomena for the maglev system.

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http://hdl.handle.net/10453/132399