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Avtomatika i Telemekhanika, 2008, Issue 1, Pages 39–44 (Mi at588)  
This article is cited in 1 scientific paper (total in 1 paper)

Deterministic Systems

The Andronov–Hopf bifurcation with weakly oscillating parameters

M. G. Yumagulova, L. S. Ibragimovaa, S. M. Muzafarova, I. D. Nurovb

a Sibai Institute (Branch of Bashkir State University)
b Institute of Mathematics, Academy of Sciences of Republic of Tajikistan, Dushanbe
Full-text PDF (184 kB) Citations (1)
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Abstract: Consideration is given to the problem of local bifurcations in neighborhoods of stationary states of dynamical systems with parameters evolving according to the periodic law. Scenarios of the bifurcation behavior of the system are studied and criteria for its stability are presented. It is shown that in the natural formulation, the Andronov–Hopf bifurcation of the dynamical system is transformed to a bifurcation of quasi-periodic oscillations. Asymptotic formulae are defined for occurring oscillations as well as recommendations for construction of solutions.
Presented by the member of Editorial Board: A. M. Krasnosel'skii

Received: 05.02.2007
English version:
Automation and Remote Control, 2008, Volume 69, Issue 1, Pages 36–41
DOI: https://doi.org/10.1134/S0005117908010049
Bibliographic databases:
Document Type: Article
PACS: 05.45.-a
Language: Russian
Citation: M. G. Yumagulov, L. S. Ibragimova, S. M. Muzafarov, I. D. Nurov, “The Andronov–Hopf bifurcation with weakly oscillating parameters”, Avtomat. i Telemekh., 2008, no. 1, 39–44; Autom. Remote Control, 69:1 (2008), 36–41
Citation in format AMSBIB
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\paper The Andronov--Hopf bifurcation with weakly oscillating parameters
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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