Topology of vibro-impact systems in the neighbourhood of grazing

Sergey Kryzhevich, Marian Wiercigroch

Research output: Contribution to journalArticlepeer-review

35 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)1919-1931
Number of pages13
JournalPhysica. D, Nonlinear Phenomena
Issue number22
Early online date24 Dec 2011
Publication statusPublished - 15 Nov 2012


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