Topology of Vibro-Impact Systems in the Neighborhood of Grazing

Details Topology of Vibro-Impact Systems in the Neighborhood of Grazing Topology of Vibro-Impact Systems in the Neighborhood of Grazing

2011-06-17

arxiv.org/abs/1106.3589v1

Mathematics

Dynamical Systems

Submitted to Physica D

Scientific paper

The grazing bifurcation is considered for the Newtonian model of vibro-impact systems. A brief review on the conditions, sufficient for 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 may be invisible or, at least, 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 the neighborhood of grazing.

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