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 Avtomat. i Telemekh.: Year: Volume: Issue: Page: Find

 Avtomat. i Telemekh., 2008, Issue 12, Pages 47–52 (Mi at763)

Deterministic Systems

The investigation algorithm of stability of periodic oscillations in the problem for the Andronov–Hopf bifurcation

N. A. Kuznetsova, M. G. Yumagulovb, I. V. Sharafutdinovb

a Kotel'nikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences, Moscow, Russia
b Sibai Institute, Bashkir State University, Sibai, Russia

Abstract: A new method for analysis of the stability of free oscillations under the conditions of the Andronov–Hopf bifurcation is suggested. In contrast to commonly applied methods, the algorithm suggested does not require the construction of integral varieties and the transition to normal forms. The algorithm is based on the comparison between the characters of stability of the stationary state of the system and the free oscillations being born. The method suggested enables us to simplify essentially the analysis of stability and obtain simple explicit criteria of stability and instability, and also define the type of bifurcation.

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English version:
Automation and Remote Control, 2008, 69:12, 2033–2038

Bibliographic databases:

PACS: 05.45.-a
Presented by the member of Editorial Board: À. Ì. Êðàñíîñåëüñêèé

Citation: N. A. Kuznetsov, M. G. Yumagulov, I. V. Sharafutdinov, “The investigation algorithm of stability of periodic oscillations in the problem for the Andronov–Hopf bifurcation”, Avtomat. i Telemekh., 2008, no. 12, 47–52; Autom. Remote Control, 69:12 (2008), 2033–2038

Citation in format AMSBIB
\Bibitem{KuzYumSha08} \by N.~A.~Kuznetsov, M.~G.~Yumagulov, I.~V.~Sharafutdinov \paper The investigation algorithm of stability of periodic oscillations in the problem for the Andronov--Hopf bifurcation \jour Avtomat. i Telemekh. \yr 2008 \issue 12 \pages 47--52 \mathnet{http://mi.mathnet.ru/at763} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2492414} \zmath{https://zbmath.org/?q=an:1165.34347} \transl \jour Autom. Remote Control \yr 2008 \vol 69 \issue 12 \pages 2033--2038 \crossref{https://doi.org/10.1134/S0005117908120035} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000263843500003} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-58149481821} 

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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. E. V. Musafirov, “Dopustimye vozmuscheniya sistemy Lengforda”, PFMT, 2016, no. 3(28), 47–51
2. Yumagulov M.G. Ibragimova L.S. Imangulova E.S., “Principal Asymptotics in the Problem on the Andronov-Hopf Bifurcation and Their Applications”, Differ. Equ., 53:12 (2017), 1578–1594
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