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Avtomatika i Telemekhanika, 2007, Issue 10, Pages 70–78 (Mi at1065)  
This article is cited in 2 scientific papers (total in 2 papers)

Stability of Systems

Statistical description of the limiting set for chaotic motions of the vibro-impact system

S. P. Gorbikov, A. V. Men'shenina

Nizhny Novgorod State University of Architecture and Civil Engineering
Full-text PDF (207 kB) Citations (2)
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Abstract: A numerical investigation of statistical properties of chaotic motions that occur in one vibro-impact system as a result of the bifurcation connected with the arrival of the periodic motion at the boundary of infinite-impact motion domain. The results of numerical computations prove the existence of a peculiar set which is limiting for chaotic motions occurred after the bifurcation. According to the numerical investigations, “the ensemble average coincides with the time average” in the neighborhood of the limiting set, i.e., it is sufficient to track only one path in solving optimization problems in such a system.
Presented by the member of Editorial Board: A. I. Kibzun

Received: 14.12.2006
English version:
Automation and Remote Control, 2007, Volume 68, Issue 10, Pages 1794–1800
DOI: https://doi.org/10.1134/S0005117907100074
Bibliographic databases:
Document Type: Article
PACS: 02.30.Oz, 47.20.Ky
Language: Russian
Citation: S. P. Gorbikov, A. V. Men'shenina, “Statistical description of the limiting set for chaotic motions of the vibro-impact system”, Avtomat. i Telemekh., 2007, no. 10, 70–78; Autom. Remote Control, 68:10 (2007), 1794–1800
Citation in format AMSBIB
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\by S.~P.~Gorbikov, A.~V.~Men'shenina
\paper Statistical description of the limiting set for chaotic motions of the vibro-impact system
\jour Avtomat. i Telemekh.
\yr 2007
\issue 10
\pages 70--78
\mathnet{http://mi.mathnet.ru/at1065}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2360028}
\zmath{https://zbmath.org/?q=an:1146.93336}
\transl
\jour Autom. Remote Control
\yr 2007
\vol 68
\issue 10
\pages 1794--1800
\crossref{https://doi.org/10.1134/S0005117907100074}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-35649024192}
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  • https://www.mathnet.ru/eng/at/y2007/i10/p70
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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