Sliding bifurcations: A novel mechanism for the sudden onset of chaos in dry friction oscillators
2003 (English)In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, ISSN 0218-1274, Vol. 13, no 10, 2935-2948 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2003. Vol. 13, no 10, 2935-2948 p.
stick-slip motion, sliding bifurcations, chaotic motion, border-collision bifurcations, dynamical-systems, motion, maps, self
IdentifiersURN: urn:nbn:se:kth:diva-23034ISI: 000187400800009OAI: oai:DiVA.org:kth-23034DiVA: diva2:341732
QC 201005252010-08-102010-08-10Bibliographically approved