Topological Behaviour of Solutions of Vibro-Impact Systems in the Neighborhood of Grazing

Sergey Kryzhevich; Marian Wiercigroch

doi:10.1016/j.physd.2011.12.009g

Topological Behaviour of Solutions of Vibro-Impact Systems in the Neighborhood of Grazing

Abstract

The grazing bifurcation is considered for the Newtonian model of vibro-impact systems. A brief review on the conditions, sufficient for the existence of a grazing family of periodic solutions, is given. The properties of these periodic solutions are discussed. A plenty of results on the topological structure of attractors of vibro-impact systems is known. However, since the considered system is strongly nonlinear, these attractors must be very sensitive to changes of parameters of the system. On the other hand, they are observed in experiments and numerical simulations. We offer (Theorem 2) an approach which allows to explain this contradiction and give a new robust mathematical model of the non-hyperbolic dynamics in a neighborhood of grazing.

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Authors (2)

Sergey Kryzhevich dr hab.
- Saint Petersburg State University
Marian Wiercigroch Professor
- University of Aberdeen

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Articles

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artykuły w czasopismach

Published in:

PHYSICA D-NONLINEAR PHENOMENA no. 241, pages 1919 - 1931,
ISSN: 0167-2789

Language:

English

Publication year:

2012

Bibliographic description:

Kryzhevich S., Wiercigroch M.: Topological Behaviour of Solutions of Vibro-Impact Systems in the Neighborhood of Grazing// PHYSICA D-NONLINEAR PHENOMENA -,iss. 22 (2012), s.1919-1931

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