Abstract
A new discontinuity-induced bifurcation, referred to as nonsmooth Hopf-type bifurcation, observed in a nonautonomous impacting hybrid systems in \(\mathbb {R}^4\) is presented. The system studied models the bouncing motion, repeated instantaneous impacts with friction, in rotating machines with magnetic bearing support. At the nonsmooth Hopf-type bifurcation point a stable regular equilibrium and two unstable small amplitude 1-impact periodic orbits arise. The existence of this bifurcation scenario depends on a complex relationship between damping, the restitution, and the friction coefficient.
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Mora, K., Budd, C. (2017). Non-smooth Hopf-Type and Grazing Bifurcations Arising from Impact/Friction Contact Events. In: Colombo, A., Jeffrey, M., Lázaro, J., Olm, J. (eds) Extended Abstracts Spring 2016. Trends in Mathematics(), vol 8. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-55642-0_23
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DOI: https://doi.org/10.1007/978-3-319-55642-0_23
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