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Through the looking-glass of the grazing bifurcation. / Ing, James; Kryzhevich, Sergey; Wiercigroch, Marian.

In: Discontinuity, Nonlinearity, and Complexity, Vol. 2, No. 3, 2013, p. 203-223.

Research output: Contribution to journal › Article › peer-review

Harvard

Ing, J, Kryzhevich, S & Wiercigroch, M 2013, 'Through the looking-glass of the grazing bifurcation', Discontinuity, Nonlinearity, and Complexity, vol. 2, no. 3, pp. 203-223. https://doi.org/10.5890/DNC.2013.08.001.

APA

Ing, J., Kryzhevich, S., & Wiercigroch, M. (2013). Through the looking-glass of the grazing bifurcation. Discontinuity, Nonlinearity, and Complexity, 2(3), 203-223. https://doi.org/10.5890/DNC.2013.08.001.

Vancouver

Ing J, Kryzhevich S, Wiercigroch M. Through the looking-glass of the grazing bifurcation. Discontinuity, Nonlinearity, and Complexity. 2013;2(3):203-223. https://doi.org/10.5890/DNC.2013.08.001.

Author

Ing, James ; Kryzhevich, Sergey ; Wiercigroch, Marian. / Through the looking-glass of the grazing bifurcation. In: Discontinuity, Nonlinearity, and Complexity. 2013 ; Vol. 2, No. 3. pp. 203-223.

BibTeX

@article{9464792f07444e80884d6c79770d625d,
title = "Through the looking-glass of the grazing bifurcation",
abstract = "It is well-known for vibro-impact systems that the existence of a periodic solution with a low-velocity impact (so-called grazing) may yield complex behavior of the solutions. In this paper we show that unstable periodic motions which pass near the delimiter without touching it may give birth to chaotic behavior of nearby solutions. We demonstrate that the number of impacts over a period of forcing varies in a small neighborhood of such periodic motions. This allows us to use the technique of symbolic dynamics. It is shown that chaos may be observed in a two-sided neighborhood of grazing and this bifurcation manifests at least two distinct ways to a complex behavior. In the second part of the paper we study the robustness of this phenomenon. Particularly, we show that the same effect can be observed in {"}soft{"} models of impacts.",
keywords = "Grazing, Homoclinic point, structural stability, models of impact",
author = "James Ing and Sergey Kryzhevich and Marian Wiercigroch",
year = "2013",
doi = "10.5890/DNC.2013.08.001.",
language = "English",
volume = "2",
pages = "203--223",
journal = "Discontinuity, Nonlinearity, and Complexity",
issn = "2164-6376",
publisher = "L & H Scientific Publishing, LLC",
number = "3",

}

RIS

TY - JOUR

T1 - Through the looking-glass of the grazing bifurcation

AU - Ing, James

AU - Kryzhevich, Sergey

AU - Wiercigroch, Marian

PY - 2013

Y1 - 2013

N2 - It is well-known for vibro-impact systems that the existence of a periodic solution with a low-velocity impact (so-called grazing) may yield complex behavior of the solutions. In this paper we show that unstable periodic motions which pass near the delimiter without touching it may give birth to chaotic behavior of nearby solutions. We demonstrate that the number of impacts over a period of forcing varies in a small neighborhood of such periodic motions. This allows us to use the technique of symbolic dynamics. It is shown that chaos may be observed in a two-sided neighborhood of grazing and this bifurcation manifests at least two distinct ways to a complex behavior. In the second part of the paper we study the robustness of this phenomenon. Particularly, we show that the same effect can be observed in "soft" models of impacts.

AB - It is well-known for vibro-impact systems that the existence of a periodic solution with a low-velocity impact (so-called grazing) may yield complex behavior of the solutions. In this paper we show that unstable periodic motions which pass near the delimiter without touching it may give birth to chaotic behavior of nearby solutions. We demonstrate that the number of impacts over a period of forcing varies in a small neighborhood of such periodic motions. This allows us to use the technique of symbolic dynamics. It is shown that chaos may be observed in a two-sided neighborhood of grazing and this bifurcation manifests at least two distinct ways to a complex behavior. In the second part of the paper we study the robustness of this phenomenon. Particularly, we show that the same effect can be observed in "soft" models of impacts.

KW - Grazing

KW - Homoclinic point

KW - structural stability

KW - models of impact

U2 - 10.5890/DNC.2013.08.001.

DO - 10.5890/DNC.2013.08.001.

M3 - Article

VL - 2

SP - 203

EP - 223

JO - Discontinuity, Nonlinearity, and Complexity

JF - Discontinuity, Nonlinearity, and Complexity

SN - 2164-6376

IS - 3

ER -

ID: 5636714