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Avtomatika i Telemekhanika, 2007, Issue 10, Pages 79–91 (Mi at1066)  

Stability of Systems

Analysis of stability in quadratic mean of the limit cycles of nonlinear stochastic systems

A. A. Gubkin, L. B. Ryashko

Ural State University, Ekaterinburg, Russia
References:
Abstract: Consideration was given to the exponential stability in quadratic mean of the stochastically perturbed limit cycles of the nonlinear systems. An approach was developed using the spectral theory of positive operators for the stability analysis. Within the framework of this approach, a positive operator of stochastic stability is assigned to the limit cycle. The spectral radius of this operator characterizes stability of the limit cycle. An iterative numerical method was proposed for calculation of the spectral radius of the stochastic stability operator, and a theorem about its convergence was proved. The constructive potentialities of the results obtained were demonstrated by the example of bifurcational analysis of the stochastic Ressler system at transition to chaos by multiple duplication of the limit cycle period.
Presented by the member of Editorial Board: A. I. Kibzun

Received: 14.12.2006
English version:
Automation and Remote Control, 2007, Volume 68, Issue 10, Pages 1801–1812
DOI: https://doi.org/10.1134/S0005117907100086
Bibliographic databases:
Document Type: Article
PACS: 02.30.Oz
Language: Russian
Citation: A. A. Gubkin, L. B. Ryashko, “Analysis of stability in quadratic mean of the limit cycles of nonlinear stochastic systems”, Avtomat. i Telemekh., 2007, no. 10, 79–91; Autom. Remote Control, 68:10 (2007), 1801–1812
Citation in format AMSBIB
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\by A.~A.~Gubkin, L.~B.~Ryashko
\paper Analysis of stability in quadratic mean of the limit cycles of nonlinear stochastic systems
\jour Avtomat. i Telemekh.
\yr 2007
\issue 10
\pages 79--91
\mathnet{http://mi.mathnet.ru/at1066}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2360029}
\zmath{https://zbmath.org/?q=an:1146.93041}
\transl
\jour Autom. Remote Control
\yr 2007
\vol 68
\issue 10
\pages 1801--1812
\crossref{https://doi.org/10.1134/S0005117907100086}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-35648943695}
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