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

G.H.M. van der Heijden

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 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 uncovered.
For a range of parameter values the sequence of bifurcations forms a
global connection between a \v{S}il'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.

*Dynamics and Stability of Systems* **15**, 159-183 (2000)