Avtomatika i Telemekhanika
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



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






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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
\Bibitem{GubRya07}
\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}
Linking options:
  • https://www.mathnet.ru/eng/at1066
  • https://www.mathnet.ru/eng/at/y2007/i10/p79
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Avtomatika i Telemekhanika
    Statistics & downloads:
    Abstract page:257
    Full-text PDF :90
    References:41
    First page:1
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024