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Nelin. Dinam., 2009, Volume 5, Number 4, Pages 603–620 (Mi nd115)  

This article is cited in 5 scientific papers (total in 5 papers)

Regular and stochastic auto-oscillations in the reological model

I. A. Bashkirtseva, A. Yu. Zubarev, L. Yu. Iskakova, L. B. Ryashko

Ural State University

Abstract: This paper is devoted to research of mathematical model of a suspension flow. For these flows, the transitions from stationary to the oscillatory regimes have been observed in experiments. Bifurcation analysis allows us to divide the space of parameters onto steady equilibria and limit cycles zones. Details of Hopf bifurcation depending on degree of system stiffness are investigated. On the basis of the stochastic sensitivity function technique, the parametrical analysis of influence of random disturbances on the system attractors is carried out. It is shown that as a system stiffness increases, the stochastic sensitivity of oscillations rises sharply. The narrow zone of super-sensitivity of oscillations was found. In this zone, even small background disturbances result in the essential fluctuations of their amplitude.

Keywords: reology, suspension, stability, sensitivity, stochastic oscillations.

Full text: PDF file (2749 kB)
UDC: 531.36
MSC: 34F05
Received: 07.05.2009

Citation: I. A. Bashkirtseva, A. Yu. Zubarev, L. Yu. Iskakova, L. B. Ryashko, “Regular and stochastic auto-oscillations in the reological model”, Nelin. Dinam., 5:4 (2009), 603–620

Citation in format AMSBIB
\Bibitem{BasZubIsk09}
\by I.~A.~Bashkirtseva, A.~Yu.~Zubarev, L.~Yu.~Iskakova, L.~B.~Ryashko
\paper Regular and stochastic auto-oscillations in the reological model
\jour Nelin. Dinam.
\yr 2009
\vol 5
\issue 4
\pages 603--620
\mathnet{http://mi.mathnet.ru/nd115}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Bordonskii G.S., Gurulev A.A., Krylov S.D., “Vliyanie temperaturnykh napryazhenii na mikrovolnovye polyarizatsionnye kharakteristiki ledyanykh pokrovov”, Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 8:2 (2011), 18–25  elib
    2. Bordonskii G.S., Gurulev A.A., Krylov S.D., Orlov A.O., Tsyrenzhapov S.V., “Dobavochnye elektromagnitnye volny v ledyanykh pokrovakh”, Led i sneg, 2011, no. 4, 71–79  elib
    3. Bashkirtseva I.A., Zubarev A.Yu., Iskakova L.Yu., Ryashko L.B., “Noise-Induced Oscillations in the Flow of Concentrated Suspensions”, Pmm-J. Appl. Math. Mech., 76:4 (2012), 466–474  crossref  mathscinet  mathscinet  isi  elib  scopus
    4. Bordonskii G.S., Tsyrenzhapov S.V., Kharin Yu.V., “Akustoelektricheskii effekt v presnom ldu”, Kondensirovannye sredy i mezhfaznye granitsy, 14:2 (2012), 162–167  elib
    5. G. S. Bordonskii, A. A. Gurulev, S. D. Krylov, “Electromagnetic loss of fresh ice in microwave range at a temperature of 0$^circ$C”, Journal of Communications Technology and Electronics, 59:6 (2014), 536–540  crossref  crossref  isi  elib  scopus
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