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

摘要

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