Teoreticheskaya i Matematicheskaya Fizika
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


TMF:
Year:
Volume:
Issue:
Page:
Find




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

Teoreticheskaya i Matematicheskaya Fizika, 2013, Volume 175, Number 1, Pages 62–83
DOI: https://doi.org/10.4213/tmf8441 (Mi tmf8441) 		 
This article is cited in 23 scientific papers (total in 23 papers)

Periodic traveling-wave-type solutions in circular chains of unidirectionally coupled equations

S. D. Glyzina, A. Yu. Kolesova, N. Kh. Rozovb

a Yaroslavl State University, Yaroslavl, Russia
b Lomonosov Moscow State University, Moscow, Russia
Full-text PDF (536 kB) Citations (23)
References:
PDF
HTML
DOI: https://doi.org/10.4213/tmf8441
Abstract: We consider special systems of ordinary differential equations, so-called circular unidirectional chains. For this class of systems, we develop a new method for studying the existence and stability problems for periodic solutions. A feature of the proposed approach is that some auxiliary systems with delay are used in both seeking cycles and analyzing their stability properties. We illustrate the relevance of this approach with a concrete example of a circular Hopfield neural network.
Keywords: chain of unidirectionally coupled equations, system with delay, Hopfield neural network, periodic solution, asymptotic behavior, stability.
Received: 14.11.2012
Revised: 23.11.2012
English version:
Theoretical and Mathematical Physics, 2013, Volume 175, Issue 1, Pages 499–517
DOI: https://doi.org/10.1007/s11232-013-0041-1
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Periodic traveling-wave-type solutions in circular chains of unidirectionally coupled equations”, TMF, 175:1 (2013), 62–83; Theoret. and Math. Phys., 175:1 (2013), 499–517
Citation in format AMSBIB
\Bibitem{GlyKolRoz13}
\by S.~D.~Glyzin, A.~Yu.~Kolesov, N.~Kh.~Rozov
\paper Periodic traveling-wave-type solutions in circular chains of unidirectionally coupled equations
\jour TMF
\yr 2013
\vol 175
\issue 1
\pages 62--83
\mathnet{http://mi.mathnet.ru/tmf8441}
\crossref{https://doi.org/10.4213/tmf8441}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3172133}
\zmath{https://zbmath.org/?q=an:06293220}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2013TMP...175..499G}
\elib{https://elibrary.ru/item.asp?id=20732601}
\transl
\jour Theoret. and Math. Phys.
\yr 2013
\vol 175
\issue 1
\pages 499--517
\crossref{https://doi.org/10.1007/s11232-013-0041-1}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000318805200005}
\elib{https://elibrary.ru/item.asp?id=20427447}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84877349653}
Linking options:
  • https://www.mathnet.ru/eng/tmf8441
  • https://doi.org/10.4213/tmf8441
  • https://www.mathnet.ru/eng/tmf/v175/i1/p62
    • This publication is cited in the following 23 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
    Statistics & downloads:
    Abstract page:814
    Full-text PDF :197
    References:77
    First page:27
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024