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Discontinuity-induced bifurcations of equilibria in piecewise-smooth and impacting dynamical systems
KTH, School of Engineering Sciences (SCI), Mechanics, Biomechanics.
2008 (English)In: Physica D: Non-linear phenomena, ISSN 0167-2789, Vol. 237, no 1, 119-136 p.Article in journal (Refereed) Published
Abstract [en]

A rich variety of dynamical scenarios has been shown to occur when a fixed point of a non-smooth map undergoes a border-collision. This paper concerns a closely related class of discontinuity-induced bifurcations, those involving equilibria of n-dimensional piecewise-smooth flows. Specifically, transitions are studied which occur when a boundary equilibrium, that is one lying within a discontinuity manifold, is perturbed. It is shown that such equilibria can either persist under parameter variations or can disappear giving rise to different bifurcation scenarios. Conditions to classify among the possible simplest scenarios are given for piecewise-smooth continuous, Filippov and impacting systems. Also, we investigate the possible birth of other attractors (e.g. limit cycles) at a boundary-equilibrium bifurcation.

Place, publisher, year, edition, pages
2008. Vol. 237, no 1, 119-136 p.
Keyword [en]
piecewise-smooth systems, bifurcations and chaos, discontinuity-induced, bifurcations, border-collision bifurcations, maps, sets
URN: urn:nbn:se:kth:diva-17333DOI: 10.1016/j.physd.2007.08.008ISI: 000253270600010ScopusID: 2-s2.0-37149040240OAI: diva2:335377
QC 20100525Available from: 2010-08-05 Created: 2010-08-05Bibliographically approved

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