Attractors near grazing-sliding bifurcations

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: http://eprints.maths.manchester.ac.uk/id/eprint/1602

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