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- Di Bernardo, M., et al.
(författare)
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Sliding bifurcations : A novel mechanism for the sudden onset of chaos in dry friction oscillators
- 2003
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Ingår i: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering. - 0218-1274. ; 13:10, s. 2935-2948
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Tidskriftsartikel (refereegranskat)abstract
- Recent investigations of nonsmooth dynamical systems have resulted in the study of a class of novel bifurcations termed as sliding bifurcations. These bifurcations are a characteristic feature of so-called Filippov systems, that is, systems of ordinary differential equations (ODEs) with discontinuous right-hand sides. In this paper we show that sliding bifurcations also play an important role in organizing the dynamics of dry friction oscillators, which are a subclass of nonsmooth systems. After introducing the possible codimension-1 sliding bifurcations of limit cycles, we show that these bifurcations organize different types of slip to stick-slip transitions in dry friction oscillators. In particular, we show both numerically and analytically that a sliding bifurcation is an important mechanism causing the sudden jump to chaos previously unexplained in the literature on friction systems. To analyze such bifurcations we make use of a new analytical method based on the study of appropriate normal form maps describing sliding bifurcations. Also, we explain the circumstances under which the theory of so-called border-collision bifurcations can be used in order to explain the onset of complex behavior in stick-slip systems.
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