Attractors near grazing-sliding bifurcations
2012 (English)In: Nonlinearity, ISSN 0951-7715, E-ISSN 1361-6544, Vol. 25, no 6, 1867-1885 p.Article in journal (Refereed) Published
In this paper we prove, for the first time, that multistability can occur in three-dimensional Fillipov type flows due to grazing-sliding bifurcations. We do this by reducing the study of the dynamics of Filippov type flows around a grazing-sliding bifurcation to the study of appropriately defined one-dimensional maps. In particular, we prove the presence of three qualitatively different types of multiple attractors born in grazing-sliding bifurcations. Namely, a period-two orbit with a sliding segment may coexist with a chaotic attractor, two stable, period-two and period-three orbits with a segment of sliding each may coexist, or a non-sliding and period-three orbit with two sliding segments may coexist.
Place, publisher, year, edition, pages
2012. Vol. 25, no 6, 1867-1885 p.
Border-Collision Bifurcations, Impact Oscillators, Systems, Chaos, Maps
IdentifiersURN: urn:nbn:se:kth:diva-99089DOI: 10.1088/0951-7715/25/6/1867ISI: 000305484500019ScopusID: 2-s2.0-84861541414OAI: oai:DiVA.org:kth-99089DiVA: diva2:541471
QC 201207182012-07-182012-07-132012-09-12Bibliographically approved