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Nelin. Dinam., 2011, Volume 7, Number 3, Pages 411–425 (Mi nd267)  

This article is cited in 12 scientific papers (total in 12 papers)

Forced synchronization of two coupled van der Pol self-oscillators

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

Kotel'nikov's Institute of Radio-Engineering and Electronics of RAS, Saratov Branch, Zelyenaya 38, Saratov, 410019, Russia

Abstract: The problem of external driving by the harmonic signal of two coupled self-oscillators is investigated. Comparison with the synchronization picture for phase oscillators is given. We discuss the configuration of periodic, two- and three-frequency regimes in the parameter space of external signal. The illustrations of three-frequency tori and resonance two-frequency tori are given. A number of significant differences from the bifurcation mechanisms for the destruction of synchronization are found compared with the case of phase oscillators.

Keywords: synchronization, bifurcations, quasi-periodic dynamics, chaos

Full text: PDF file (1087 kB)
References: PDF file   HTML file
UDC: 517.9
MSC: 39Axx, 93D05
Received: 04.07.2011
Accepted:09.08.2011

Citation: A. P. Kuznetsov, I. R. Sataev, L. V. Turukina, “Forced synchronization of two coupled van der Pol self-oscillators”, Nelin. Dinam., 7:3 (2011), 411–425

Citation in format AMSBIB
\Bibitem{KuzSatTur11}
\by A.~P.~Kuznetsov, I.~R.~Sataev, L.~V.~Turukina
\paper Forced synchronization of two coupled van der Pol self-oscillators
\jour Nelin. Dinam.
\yr 2011
\vol 7
\issue 3
\pages 411--425
\mathnet{http://mi.mathnet.ru/nd267}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Tyuryukina L.V., Chernyshov N.Yu., “Sinkhronizatsiya vozbuzhdaemykh reaktivno svyazannykh fazovykh ostsillyatorov”, Izvestiya vysshikh uchebnykh zavedenii. Prikladnaya nelineinaya dinamika, 20:1 (2012), 81–90  zmath  elib
    2. A. P. Kuznetsov, M. V. Pozdnyakov, Yu. V. Sedova, “Svyazannye universalnye otobrazheniya s bifurkatsiei Neimarka–Sakera”, Nelineinaya dinam., 8:3 (2012), 473–482  mathnet
    3. 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
    4. E. N. Peregorodova, S. A. Usacheva, N. M. Ryskin, “K teorii vynuzhdennoi sinkhronizatsii avtomodulyatsionnykh kolebanii”, Nelineinaya dinam., 8:5 (2012), 913–929  mathnet
    5. 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
    6. Quantum Electron., 44:1 (2014), 17–22  mathnet  crossref  adsnasa  isi  elib
    7. G. A. Rustamov, “Sinkhronizatsiya neidentichnykh dinamicheskikh sistem s pomoschyu robastnogo ekvivalentnogo upravleniya”, Izvestiya Tomskogo politekhnicheskogo universiteta, 325:5 (2014), 33–44  elib
    8. 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
    9. A. P. Gulai, A. V. Bukh, “Issledovanie multistabilnosti i vynuzhdennoi sinkhronizatsii v neavtonomnoi sisteme dvukh ostsillyatorov Van der Polya s ottalkivayuschim vzaimodeistviem”, Izvestiya vysshikh uchebnykh zavedenii. Prikladnaya nelineinaya dinamika, 22:6 (2014), 94–103  elib
    10. V. N. Tkhai, “Model containing coupled subsystems with oscillations of different types”, Autom. Remote Control, 78:4 (2017), 595–607  mathnet  crossref  mathscinet  isi  elib
    11. I. N. Barabanov, V. N. Tkhai, “Stabilization of oscillations in a periodic system by choosing appropriate couplings”, Autom. Remote Control, 79:12 (2018), 2128–2135  mathnet  crossref  crossref  isi  elib
    12. V. N. Tkhai, “Periodicheskaya model, soderzhaschaya svyazannye podsistemy s razlichnymi tipami kolebanii”, Avtomat. i telemekh., 2019, no. 3, 55–67  mathnet  crossref  elib
  • Нелинейная динамика
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