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Bifurcation sequences in the interaction of resonances in a model deriving from nonlinear rotordynamics: the zipper

van der Heijden, GHM; (2000) Bifurcation sequences in the interaction of resonances in a model deriving from nonlinear rotordynamics: the zipper. Dynamics and Stability of Systems , 15 (2) 159 - 183. 10.1080/713603734.

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Abstract

Using numerical continuation we show a new bifurcation scenario involving resonant periodic orbits in a parametrised four-dimensional autonomous system deriving from nonlinear rotordynamics. the scenario consists of a carefully orchestrated sequence of transcritical bifurcations in which branches or periodic solutions are exchanged. Collectively, the bifurcations resemble the action of a zipper. An underlying governing mechanism clearly exists but still has to be uncovered. For a range of parameter values the sequence of bifurcations forms a global connection between a Sil'nikov bifurcation and (partial) mode-locking. The homoclinic bifurcation is introduced into the system by a Takens-Bogdanov bifurcation. The system also features an interaction between two chaotic Sil'nikov bifurcations

Type:Article
Title:Bifurcation sequences in the interaction of resonances in a model deriving from nonlinear rotordynamics: the zipper
DOI:10.1080/713603734
Keywords:chaos, CONNECTION, FEATURES, Form, global, homoclinic orbit, interaction, MECHANISM, mode-lockin, model, nonlinear, nonlinear rotordynamic, numerical, PARAMETER, RANGE, resonance, resonances, SEQUENCE, SEQUENCES, Sil'nikov bifurcation, Solutions, SYSTEM, VALUES
UCL classification:UCL > School of BEAMS > Faculty of Engineering Science > Civil, Environmental and Geomatic Engineering

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