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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics]
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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics], 2010, Volume 6, Number 4, Pages 693–717 (Mi nd1)  
This article is cited in 14 scientific papers (total in 14 papers)

Synchronization and multi-frequency oscillations in the chain of phase oscillators

A. P. Kuznetsov, I. R. Sataev, L. V. Turukina

Saratov Branch of the Institute of Radio Engineering and Electronics
Full-text PDF (141755 kB) Citations (14)
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Abstract: The problem of the dynamics of phase oscillators is discussed with an increasing their numbers. We discuss the organization of the parameters plane responsible for the frequency detunings of the oscillators and amplitude of the dissipative coupled. The region of complete synchronization, quasi-periodic oscillations of different dimension and chaos are are observed. We discuss the changing of the synchronization picture with an increasing of the number of oscillators in the chain. We use the method of charts of Lyapunov exponents and modification of the method of charts of dynamical regimes visualized two-frequency resonant tori of different types.
Keywords: synchronization, phase oscillators, quasi-periodical dynamics, chaos.
Received: 28.06.2010
Document Type: Article
UDC: 517.9
MSC: 39Axx, 93D05
Language: Russian
Citation: A. P. Kuznetsov, I. R. Sataev, L. V. Turukina, “Synchronization and multi-frequency oscillations in the chain of phase oscillators”, Nelin. Dinam., 6:4 (2010), 693–717
Citation in format AMSBIB
\Bibitem{KuzSatTur10}
\by A.~P.~Kuznetsov, I.~R.~Sataev, L.~V.~Turukina
\paper Synchronization and multi-frequency oscillations in the chain of phase oscillators
\jour Nelin. Dinam.
\yr 2010
\vol 6
\issue 4
\pages 693--717
\mathnet{http://mi.mathnet.ru/nd1}
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  • https://www.mathnet.ru/eng/nd1
  • https://www.mathnet.ru/eng/nd/v6/i4/p693
    • This publication is cited in the following 14 articles:
    1. M. A. Kovaleva, V. V. Smirnov, L. I. Manevich, “Statsionarnaya i nestatsionarnaya dinamika sistemy dvukh garmonicheski svyazannykh mayatnikov”, Nelineinaya dinam., 13:1 (2017), 105–115  mathnet  crossref  elib
    2. Quantum Electron., 44:1 (2014), 17–22  mathnet  crossref  adsnasa  isi  elib
    3. A. P. Kuznetsov, L. V. Tyuryukina, I. R. Sataev, N. Yu. Chernyshov, “Sinkhronizatsiya i mnogochastotnaya kvaziperiodichnost v dinamike svyazannykh ostsillyatorov”, Izvestiya vysshikh uchebnykh zavedenii. Prikladnaya nelineinaya dinamika, 22:1 (2014), 27–54  zmath  elib
    4. A. I. Ivanov, “Ostsillyatornaya model vzaimodeistvii vnutri maloi sotsialnoi gruppy v promyshlennosti i transporte”, Nauchnyi vestnik Moskovskogo gosudarstvennogo tekhnicheskogo universiteta grazhdanskoi aviatsii, 2014, no. 204, 123–129  elib
    5. E. V. Kurilova, “Sinkhronizatsiya kolebanii v dinamike chislennosti dvukh migratsionno svyazannykh soobschestv «khischnik-zhertva»”, Regionalnye problemy, 17:2 (2014), 35–39  elib
    6. A. P. Kuznetsov, L. V. Tyuryukina, N. Yu. Chernyshov, “Sinkhronizatsiya i kvaziperiodicheskie kolebaniya trekh reaktivno svyazannykh ostsillyatorov”, Nelineinaya dinam., 9:1 (2013), 11–25  mathnet
    7. Kuznetsov A.P., Sataev I.R., Sedova Yu.V., Tyuryukina L.V., “O modelirovanii dinamiki svyazannykh avtokolebatelnykh ostsillyatorov s pomoschyu prosteishikh fazovykh otobrazhenii”, Izvestiya vysshikh uchebnykh zavedenii. Prikladnaya nelineinaya dinamika, 20:2 (2012), 112–137  mathscinet  zmath  elib
    8. A. P. Kuznetsov, M. V. Pozdnyakov, Yu. V. Sedova, “Svyazannye universalnye otobrazheniya s bifurkatsiei Neimarka–Sakera”, Nelineinaya dinam., 8:3 (2012), 473–482  mathnet
    9. Borisov A.V. Jalnine A.Yu. Kuznetsov S.P. Sataev I.R. Sedova J.V., “Dynamical Phenomena Occurring Due to Phase Volume Compression in Nonholonomic Model of the Rattleback”, Regul. Chaotic Dyn., 17:6 (2012), 512–532  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    10. S. P. Kuznetsov, A. Yu. Zhalnin, I. R. Sataev, Yu. V. Sedova, “Fenomeny nelineinoi dinamiki dissipativnykh sistem v negolonomnoi mekhanike «keltskogo kamnya»”, Nelineinaya dinam., 8:4 (2012), 735–762  mathnet
    11. A. P. Kuznetsov, S. P. Kuznetsov, L. V. Tyuryukina, I. R. Sataev, “Stsenarii Landau–Khopfa v ansamble vzaimodeistvuyuschikh ostsillyatorov”, Nelineinaya dinam., 8:5 (2012), 863–873  mathnet
    12. E. N. Peregorodova, S. A. Usacheva, N. M. Ryskin, “K teorii vynuzhdennoi sinkhronizatsii avtomodulyatsionnykh kolebanii”, Nelineinaya dinam., 8:5 (2012), 913–929  mathnet
    13. A. P. Kuznetsov, I. R. Sataev, L. V. Tyuryukina, “Vynuzhdennaya sinkhronizatsiya dvukh svyazannykh avtokolebatelnykh ostsillyatorov Van der Polya”, Nelineinaya dinam., 7:3 (2011), 411–425  mathnet
    14. Emelyanova Yu.P., Kuznetsov A.P., Tyuryukina L.V., “Dinamika trekh neidentichnykh po upravlyayuschim parametram svyazannykh ostsillyatorov van der polya”, Izvestiya vysshikh uchebnykh zavedenii. Prikladnaya nelineinaya dinamika, 19:5 (2011), 76–90  zmath  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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