Glendinning, P. and Kowalcyk, P. and Nordmark, A.B. (2011) Attractors near grazing-sliding bifurcations. [MIMS Preprint]
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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 2010, the AIP's Physics and Astronomy Classification Scheme > 00 GENERAL PHYSICS > 02 Mathematical methods in physics PACS 2010, the AIP's Physics and Astronomy Classification Scheme > 00 GENERAL PHYSICS > 05 Statistical physics, thermodynamics, and nonlinear dynamical systems |
| Depositing User: | Ms Lucy van Russelt |
| Date Deposited: | 07 Apr 2011 |
| Last Modified: | 08 Nov 2017 18:18 |
| URI: | https://eprints.maths.manchester.ac.uk/id/eprint/1602 |
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