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2011.29: Attractors near grazing-sliding bifurcations

2011.29: P. Glendinning, P. Kowalcyk and A.B. Nordmark (2011) Attractors near grazing-sliding bifurcations.

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Abstract

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 appropri- ately 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 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.

Item Type:MIMS Preprint
Uncontrolled Keywords:Multiple attractors, grazing-sliding bifurcations, one-dimensional maps;
Subjects:PACS 2003 > 02 Mathematical methods in physics
PACS 2003 > 05 Statistical physics, thermodynamics, and nonlinear dynamical systems
MIMS number:2011.29
Deposited By:Ms Lucy van Russelt
Deposited On:07 April 2011

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