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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2007, Volume 259, Pages 10–19 (Mi tm566)  
This article is cited in 1 scientific paper (total in 1 paper)

Soft Loss of Stability in an Ocean Circulation Box Model with Turbulent Fluxes

A. A. Davydovab, N. B. Melnikovcbd

a Vladimir State University
b International Institute for Applied Systems Analysis
c M. V. Lomonosov Moscow State University
d Central Economics and Mathematics Institute, RAS
Full-text PDF (190 kB) Citations (1)
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Abstract: For a 2D system of ordinary differential equations that gives a qualitative description of the thermohaline circulation in the ocean, we prove the existence of a limit cycle for a large class of transfer functions. We show that this cycle arises in the system as a result of the soft loss of stability of a steady state when a step transfer function is smoothed by functions from the above-mentioned class.
Received in January 2007
English version:
Proceedings of the Steklov Institute of Mathematics, 2007, Volume 259, Pages 6–15
DOI: https://doi.org/10.1134/S0081543807040025
Bibliographic databases:
UDC: 517.9
Language: Russian
Citation: A. A. Davydov, N. B. Melnikov, “Soft Loss of Stability in an Ocean Circulation Box Model with Turbulent Fluxes”, Analysis and singularities. Part 2, Collected papers. Dedicated to academician Vladimir Igorevich Arnold on the occasion of his 70th birthday, Trudy Mat. Inst. Steklova, 259, Nauka, MAIK «Nauka/Inteperiodika», M., 2007, 10–19; Proc. Steklov Inst. Math., 259 (2007), 6–15
Citation in format AMSBIB
\Bibitem{DavMel07}
\by A.~A.~Davydov, N.~B.~Melnikov
\paper Soft Loss of Stability in an Ocean Circulation Box Model with Turbulent Fluxes
\inbook Analysis and singularities. Part~2
\bookinfo Collected papers. Dedicated to academician Vladimir Igorevich Arnold on the occasion of his 70th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2007
\vol 259
\pages 10--19
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm566}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2433674}
\zmath{https://zbmath.org/?q=an:1153.76032}
\elib{https://elibrary.ru/item.asp?id=9572725}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2007
\vol 259
\pages 6--15
\crossref{https://doi.org/10.1134/S0081543807040025}
\elib{https://elibrary.ru/item.asp?id=13559702}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-38849105019}
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  • https://www.mathnet.ru/eng/tm566
  • https://www.mathnet.ru/eng/tm/v259/p10
    • This publication is cited in the following 1 articles:
    1. A. A. Davydov, S. O. Zosimov, “Typical Occurrence of Self-oscillations in an Ocean Circulation Box Model with Turbulent Fluxes”, Proc. Steklov Inst. Math., 321 (2023), 107–116  mathnet  crossref  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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