RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Nelin. Dinam.:
Year:
Volume:
Issue:
Page:
Find






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


Nelin. Dinam., 2017, Volume 13, Number 2, Pages 151–164 (Mi nd557)  

Original papers

Bifurcational mechanism of formation of developed multistability in a van der Pol oscillator with time-delayed feedback

B. I. Maksima, N. M. Ryskinb

a Yuri Gagarin State Technical University of Saratov, ul. Politechnicheskaya 77, Saratov, 410054, Russia
b National Research Saratov State University, ul. Astrakhanskaya 83, Saratov, 410012, Russia

Abstract: The mechanism of formation of multistability in a van der Pol generator with time-delayed feedback is studied. It is found that the developed multistability is formed through a sequence of two types of bifurcations: supercritical AndronovHopf bifurcation and subcritical NeimarkSacker bifurcation. With variation of the control parameters, the fixed point repeatedly undergoes supercritical AndronovHopf bifurcation, which leads to an increase in the number of saddle cycles. The limit cycles acquire stability after a number of subcritical Neimark Sacker bifurcations. The dynamics of the system is studied in a wide range of control parameters values.

Keywords: Time delay, bifurcations, multistability

Funding Agency Grant Number
Russian Foundation for Basic Research 16-37-00104 _


DOI: https://doi.org/10.20537/nd1702001

Full text: PDF file (839 kB)
References: PDF file   HTML file

Document Type: Article
UDC: 537.86/.87:530.182
MSC: 37M20
Received: 18.03.2017
Accepted:10.04.2017

Citation: B. I. Maksim, N. M. Ryskin, “Bifurcational mechanism of formation of developed multistability in a van der Pol oscillator with time-delayed feedback”, Nelin. Dinam., 13:2 (2017), 151–164

Citation in format AMSBIB
\Bibitem{MakRys17}
\by B.~I.~Maksim, N.~M.~Ryskin
\paper Bifurcational mechanism of formation of developed multistability in a van der Pol oscillator with time-delayed feedback
\jour Nelin. Dinam.
\yr 2017
\vol 13
\issue 2
\pages 151--164
\mathnet{http://mi.mathnet.ru/nd557}
\crossref{https://doi.org/10.20537/nd1702001}
\elib{http://elibrary.ru/item.asp?id=29443374}


Linking options:
  • http://mi.mathnet.ru/eng/nd557
  • http://mi.mathnet.ru/eng/nd/v13/i2/p151

    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
  • Number of views:
    This page:101
    Full text:37
    References:12

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019