Regular and Chaotic Dynamics
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



Regul. Chaotic Dyn.:
Year:
Volume:
Issue:
Page:
Find






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


Regular and Chaotic Dynamics, 2019, Volume 24, Issue 6, Pages 725–738
DOI: https://doi.org/10.1134/S1560354719060108
(Mi rcd1036)
 

This article is cited in 1 scientific paper (total in 1 paper)

Topaj – Pikovsky Involution in the Hamiltonian Lattice of Locally Coupled Oscillators

Vyacheslav P. Kruglovabc, Sergey P. Kuznetsovcb

a Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
b Kotelnikov’s Institute of Radio-Engineering and Electronics of RAS, Saratov Branch, ul. Zelenaya 38, Saratov, 410019 Russia
c Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia
Citations (1)
References:
Abstract: We discuss the Hamiltonian model of an oscillator lattice with local coupling. The Hamiltonian model describes localized spatial modes of nonlinear the Schrödinger equation with periodic tilted potential. The Hamiltonian system manifests reversibility of the Topaj – Pikovsky phase oscillator lattice. Furthermore, the Hamiltonian system has invariant manifolds with asymptotic dynamics exactly equivalent to the Topaj – Pikovsky model. We examine the stability of trajectories belonging to invariant manifolds by means of numerical evaluation of Lyapunov exponents. We show that there is no contradiction between asymptotic dynamics on invariant manifolds and conservation of phase volume of the Hamiltonian system. We demonstrate the complexity of dynamics with results of numerical simulations.
Keywords: reversibility, involution, Hamiltonian system, Topaj – Pikovsky model, phase oscillator lattice.
Funding agency Grant number
Russian Science Foundation 15-12-20035
19-71-30012
The work of V. P.Kruglov and S.P.Kuznetsov was supported by the grant of the Russian Science Foundation (project no. 15-12-20035) (formulation of the problem, analytical calculations and research of related topics (Sections 1 and 2)). The work of V. P.Kruglov was supported by the grant of the Russian Science Foundation (project no. 19-71-30012) (analytical and numerical calculations and interpretation of obtained results (Sections 3–6)).
Received: 28.10.2019
Accepted: 11.11.2019
Bibliographic databases:
Document Type: Article
Language: English
Citation: Vyacheslav P. Kruglov, Sergey P. Kuznetsov, “Topaj – Pikovsky Involution in the Hamiltonian Lattice of Locally Coupled Oscillators”, Regul. Chaotic Dyn., 24:6 (2019), 725–738
Citation in format AMSBIB
\Bibitem{KruKuz19}
\by Vyacheslav P. Kruglov, Sergey P. Kuznetsov
\paper Topaj – Pikovsky Involution in the Hamiltonian Lattice of Locally Coupled Oscillators
\jour Regul. Chaotic Dyn.
\yr 2019
\vol 24
\issue 6
\pages 725--738
\mathnet{http://mi.mathnet.ru/rcd1036}
\crossref{https://doi.org/10.1134/S1560354719060108}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4040817}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000511339400010}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85076360394}
Linking options:
  • https://www.mathnet.ru/eng/rcd1036
  • https://www.mathnet.ru/eng/rcd/v24/i6/p725
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024