Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Zh. Vychisl. Mat. Mat. Fiz.:
Year:
Volume:
Issue:
Page:
Find




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

Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2013, Volume 53, Number 5, Pages 737–743
DOI: https://doi.org/10.7868/S0044466913050074 (Mi zvmmf9854) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Features of the behavior of solutions to a nonlinear dynamical system in the case of two-frequency parametric resonance

A. Yu. Koverga, E. P. Kubyshkin

P. G. Demidov Yaroslavl State University
Full-text PDF (428 kB) Citations (2)
References:
PDF
HTML
DOI: https://doi.org/10.7868/S0044466913050074
Abstract: Two-frequency parametric resonance in nonlinear dynamical systems is studied by analyzing a delay differential equation with the delay obeying a two-frequency law, which arises in the mathematical simulation of some physical processes. It is shown that the system can exhibit chaotic oscillations (strange attractors) when the parametric excitation frequencies are both close to the doubled eigenfrequency of the system (degenerate case). The formation mechanisms of chaotic attractors are discussed, and the Lyapunov exponents and the Lyapunov dimension are calculated for them. If only one of the parametric excitation frequencies is close to the double eigenfrequency, a two-frequency regime occurs in the system.
Key words: delay differential equations, parametric resonance in nonlinear dynamical systems, chaotic oscillations, strange attractor.
Received: 18.11.2011
Revised: 09.12.2012
English version:
Computational Mathematics and Mathematical Physics, 2013, Volume 53, Issue 5, Pages 573–579
DOI: https://doi.org/10.1134/S0965542513050060
Bibliographic databases:
Document Type: Article
UDC: 519.62
Language: Russian
Citation: A. Yu. Koverga, E. P. Kubyshkin, “Features of the behavior of solutions to a nonlinear dynamical system in the case of two-frequency parametric resonance”, Zh. Vychisl. Mat. Mat. Fiz., 53:5 (2013), 737–743; Comput. Math. Math. Phys., 53:5 (2013), 573–579
Citation in format AMSBIB
\Bibitem{KovKub13}
\by A.~Yu.~Koverga, E.~P.~Kubyshkin
\paper Features of the behavior of solutions to a nonlinear dynamical system in the case of two-frequency parametric resonance
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2013
\vol 53
\issue 5
\pages 737--743
\mathnet{http://mi.mathnet.ru/zvmmf9854}
\crossref{https://doi.org/10.7868/S0044466913050074}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3253190}
\elib{https://elibrary.ru/item.asp?id=19002266}
\transl
\jour Comput. Math. Math. Phys.
\yr 2013
\vol 53
\issue 5
\pages 573--579
\crossref{https://doi.org/10.1134/S0965542513050060}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000319418500005}
\elib{https://elibrary.ru/item.asp?id=20435543}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84878302762}
Linking options:
  • https://www.mathnet.ru/eng/zvmmf9854
  • https://www.mathnet.ru/eng/zvmmf/v53/i5/p737
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
    Statistics & downloads:
    Abstract page:279
    Full-text PDF :59
    References:46
    First page:17
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024