Attractors near grazing-sliding bifurcations

作者：Glendinning P^*; Kowalczyk P; Nordmark A B

来源：Nonlinearity, 2012, 25(6): 1867-1885.

DOI：10.1088/0951-7715/25/6/1867

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.

• 出版日期2012-6