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Avtomat. i Telemekh., 2008, Issue 1, Pages 39–44 (Mi at588)  

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

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.

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English version:
Automation and Remote Control, 2008, 69:1, 36–41

Bibliographic databases:

PACS: 05.45.-a
Presented by the member of Editorial Board: А. М. Красносельский

Received: 05.02.2007

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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\issue 1
\pages 39--44
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\jour Autom. Remote Control
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