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Bifurcations in Non...
Bifurcations in Nonsmooth Dynamical Systems
- Article/chapterEnglish2008
Publisher, publication year, extent ...
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Society for Industrial & Applied Mathematics (SIAM),2008
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printrdacarrier
Numbers
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LIBRIS-ID:oai:DiVA.org:kth-17974
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https://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-17974URI
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https://doi.org/10.1137/050625060DOI
Supplementary language notes
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Language:English
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Summary in:English
Part of subdatabase
Classification
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Subject category:ref swepub-contenttype
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Subject category:for swepub-publicationtype
Notes
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QC 20100525
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A review is presented of the one-parameter, nonsmooth bifurcations that occur in a variety of continuous-time piecewise-smooth dynamical systems. Motivated by applications, a pragmatic approach is taken to defining a discontinuity-induced bifurcation (DIB) as a nontrivial interaction of a limit set with respect to a codimension-one discontinuity boundary in phase space. Only DIBs that are local are considered, that is, bifurcations involving equilibria or a single point of boundary interaction along a limit cycle for flows. Three classes of systems are considered, involving either state jumps, jumps in the vector field, or jumps in some derivative of the vector field. A rich array of dynamics are revealed, involving the sudden creation or disappearance of attractors, jumps to chaos, bifurcation diagrams with sharp corners, and cascades of period adding. For each kind of bifurcation identified, where possible, a kind of "normal form" or discontinuity mapping (DM) is given, together with a canonical example and an application. The goal is always to explain dynamics that may be observed in simulations of systems which include friction oscillators, impact oscillators, DC-DC converters, and problems in control theory.
Subject headings and genre
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nonsmooth
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dynamical system
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bifurcation
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discontinuity
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piecewise
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equilibria
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limit cycles
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border-collision bifurcations
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piecewise-smooth systems
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stick-slip
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vibrations
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grazing bifurcations
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impact oscillators
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linear-oscillator
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sliding bifurcations
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mechanical systems
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buck
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converter
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dry friction
Added entries (persons, corporate bodies, meetings, titles ...)
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Budd, C. J.
(author)
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Champneys, A. R.
(author)
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Kowalczyk, P.
(author)
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Nordmark, Arne B.KTH,Biomekanik(Swepub:kth)u1g6ocyk
(author)
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Tost, G. O.
(author)
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Piiroinen, P. T.
(author)
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KTHBiomekanik
(creator_code:org_t)
Related titles
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In:SIAM Review: Society for Industrial & Applied Mathematics (SIAM)50:4, s. 629-7010036-14451095-7200
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