Attractors near grazing–sliding bifurcations

P Glendinning, P Kowalczyk, A B Nordmark
2012 Nonlinearity  
In this paper we prove, for the first time, that multistability can occur in 3-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
more » ... ent may coexsist 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.
doi:10.1088/0951-7715/25/6/1867 fatcat:plcn5v3pljbjld5nqxqjjucaki