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Invariant polygons in systems with grazing-sliding

Chaos 18, 023121 (2008); doi:10.1063/1.2904774

Published 5 June 2008

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R. Szalai and H. M. Osinga
Bristol Centre for Applied Nonlinear Mathematics, University of Bristol, University Walk, Bristol, BS8 1TR, United Kingdom
The paper investigates generic three-dimensional nonsmooth systems with a periodic orbit near grazing-sliding. We assume that the periodic orbit is unstable with complex multipliers so that two dominant frequencies are present in the system. Because grazing-sliding induces a dimension loss and the instability drives every trajectory into sliding, the system has an attractor that consists of forward sliding orbits. We analyze this attractor in a suitably chosen Poincaré section using a three-parameter generalized map that can be viewed as a normal form. We show that in this normal form the attractor must be contained in a finite number of lines that intersect in the vertices of a polygon. However the attractor is typically larger than the associated polygon. We classify the number of lines involved in forming the attractor as a function of the parameters. Furthermore, for fixed values of parameters we investigate the one-dimensional dynamics on the attractor. ©2008 American Institute of Physics
History: Received 7 August 2007; accepted 6 March 2008; published 5 June 2008
Permalink: http://link.aip.org/link/?CHAOEH/18/023121/1
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KEYWORDS and PACS

Keywords
PACS
  • 05.45.-a
    Nonlinear dynamics and chaos
  • YEAR: 2008

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PUBLICATION DATA

ISSN:
1054-1500 (print)   1089-7682 (online)
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