Through the looking-glass of the grazing bifurcation: Part I - Theoretical framework

Details Through the looking-glass of the grazing bifurcation: Part I - Theoretical framework Through the looking-glass of the grazing bifurcation: Part I - Theoretical framework

2011-12-26

arxiv.org/abs/1112.5841v1

Mathematics

Dynamical Systems

28 pages, 5 figures

Scientific paper

It is well-known and demonstrated in many papers that for vibro-impact systems an existence of a periodic solution with a low-velocity impact may yield a complex behavior of solutions. The limit case, i.e. existence of a periodic solution with a zero-velocity impact is called grazing. Slightly changing the parameters of a system with grazing, we may obtain a periodic solution which passes near the delimiter without touching it. In this paper we show that sometimes existence of these solutions can provide chaos.

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