A codimension-two scenario of sliding solutions in grazing-sliding bifurcations
2006 (English)In: Nonlinearity, ISSN 0951-7715, E-ISSN 1361-6544, Vol. 19, no 1, 1-26 p.Article in journal (Refereed) Published
This paper investigates codimension-two bifurcations that involve grazing-sliding and fold scenarios. An analytical unfolding of this novel codimension-two bifurcation is presented. Using the discontinuity mapping techniques it is shown that the fold curve is one-sided and cubically tangent to the grazing curve locally to the codimension-two point. This theory is then applied to explain the dynamics of a dry-friction oscillator where such a codimension-two point has been found. In particular, the presence and the character of essential bifurcation curves that merge at the codimension-two point are confirmed. This allows us to study the dynamics away from the codimension-two point using a piecewise affine approximation of the normal form for grazing-sliding bifurcations and explain the dynamics observed in the friction system.
Place, publisher, year, edition, pages
2006. Vol. 19, no 1, 1-26 p.
border collision bifurcations, friction oscillators, systems, chaos
IdentifiersURN: urn:nbn:se:kth:diva-15398DOI: 10.1088/0951-7715/19/1/001ISI: 000234980600002ScopusID: 2-s2.0-29144489480OAI: oai:DiVA.org:kth-15398DiVA: diva2:333439
QC 201005252010-08-052010-08-05Bibliographically approved