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


Zh. Vychisl. Mat. Mat. Fiz., 2018, Volume 58, Number 3, Pages 403–413 (Mi zvmmf10692)  

Search for periodic solutions of highly nonlinear dynamical systems

L. F. Petrov

Plekhanov Russian University of Economics, Moscow, Russia

Abstract: Numerical-analytical methods for finding periodic solutions of highly nonlinear autonomous and nonautonomous systems of ordinary differential equations are considered. Algorithms for finding initial conditions corresponding to a periodic solution are proposed. The stability of the found periodic solutions is analyzed using corresponding variational systems. The possibility of studying the evolution of periodic solutions in a strange attractor zone and on its boundaries is discussed, and interactive software implementations of the proposed algorithms are described. Numerical examples are given.

Key words: highly nonlinear systems of ordinary differential equations, periodic solutions, stability of periodic solutions, strange attractor, deterministic chaos.

DOI: https://doi.org/10.7868/S0044466918030080

References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2018, 58:3, 384–393

Bibliographic databases:

UDC: 519.624
Received: 30.01.2017
Revised: 20.04.2017

Citation: L. F. Petrov, “Search for periodic solutions of highly nonlinear dynamical systems”, Zh. Vychisl. Mat. Mat. Fiz., 58:3 (2018), 403–413; Comput. Math. Math. Phys., 58:3 (2018), 384–393

Citation in format AMSBIB
\Bibitem{Pet18}
\by L.~F.~Petrov
\paper Search for periodic solutions of highly nonlinear dynamical systems
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2018
\vol 58
\issue 3
\pages 403--413
\mathnet{http://mi.mathnet.ru/zvmmf10692}
\crossref{https://doi.org/10.7868/S0044466918030080}
\elib{https://elibrary.ru/item.asp?id=32615744}
\transl
\jour Comput. Math. Math. Phys.
\yr 2018
\vol 58
\issue 3
\pages 384--393
\crossref{https://doi.org/10.1134/S0965542518030089}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000430012700008}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85045391620}


Linking options:
  • http://mi.mathnet.ru/eng/zvmmf10692
  • http://mi.mathnet.ru/eng/zvmmf/v58/i3/p403

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
    Number of views:
    This page:172
    References:41

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021