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.
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Original Russian Text © S.P. Gorbikov, A.V. Men’shenina, 2007, published in Avtomatika i Telemekhanika, 2007, No. 10, pp. 70–78.
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Gorbikov, S.P., Men’shenina, A.V. Statistical description of the limiting set for chaotic motions of the vibro-impact system. Autom Remote Control 68, 1794–1800 (2007). https://doi.org/10.1134/S0005117907100074
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DOI: https://doi.org/10.1134/S0005117907100074