Stability and dynamics of a controlled van der Pol-Duffing oscillator

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dc.contributor.authorJi, J.
dc.contributor.authorHansen, C.
dc.contributor.conferenceDCDIS International Conference on Engineering Applications and Computational Algorithms (4th : 2005 : Guelph, Ontario, Canada)
dc.date.issued2006
dc.description.abstractThe trivial equilibrium of a van der Pol–Duffing oscillator under a linear-plus-nonlinear feedback control may change its stability either via a single or via a double Hopf bifurcation if the time delay involved in the feedback reaches certain values. It is found that the trivial equilibrium may lose its stability via a subcritical or supercritical Hopf bifurcation and regain its stability via a reverse subcritical or supercritical Hopf bifurcation as the time delay increases. A stable limit cycle appears after a supercritical Hopf bifurcation occurs and disappears through a reverse supercritical Hopf bifurcation. The interaction of the weakly periodic excitation and the stable bifurcating solution is investigated for the forced system under primary resonance conditions. It is shown that the forced periodic response may lose its stability via a Neimark–Sacker bifurcation. Analytical results are validated by a comparison with those of direct numerical integration.
dc.description.statementofresponsibilityJ. C. Ji and C. H. Hansen
dc.description.urihttp://www.elsevier.com/wps/find/journaldescription.cws_home/967/description#description
dc.identifier.citationChaos, Solitons and Fractals, 2006; 28(2):555-570
dc.identifier.doi10.1016/j.chaos.2005.08.021
dc.identifier.issn0960-0779
dc.identifier.issn1873-2887
dc.identifier.orcidHansen, C. [0000-0002-1444-4716]
dc.identifier.urihttp://hdl.handle.net/2440/22864
dc.language.isoen
dc.publisherPergamon-Elsevier Science Ltd
dc.publisher.placeWATAM PRESS, C/O DCDIS JOURNAL, 317 KAREN PLACE, WATERLOO, ONTARIO N2L 6K8, CANADA
dc.source.urihttps://doi.org/10.1016/j.chaos.2005.08.021
dc.titleStability and dynamics of a controlled van der Pol-Duffing oscillator
dc.typeJournal article
pubs.publication-statusPublished

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