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Avtomatika i Telemekhanika, 2008, Issue 12, Pages 47–52 (Mi at763)  
This article is cited in 2 scientific papers (total in 2 papers)

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
Full-text PDF (178 kB) Citations (2)
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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.
Presented by the member of Editorial Board: A. M. Krasnosel'skii

Received: 02.07.2008
English version:
Automation and Remote Control, 2008, Volume 69, Issue 12, Pages 2033–2038
DOI: https://doi.org/10.1134/S0005117908120035
Bibliographic databases:
Document Type: Article
PACS: 05.45.-a
Language: Russian
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
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\paper The investigation algorithm of stability of periodic oscillations in the problem for the Andronov--Hopf bifurcation
\jour Avtomat. i Telemekh.
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\pages 47--52
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\jour Autom. Remote Control
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\crossref{https://doi.org/10.1134/S0005117908120035}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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