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Nelin. Dinam., 2009, Volume 5, Number 2, Pages 237–252 (Mi nd91)  

This article is cited in 25 scientific papers (total in 25 papers)

Numerical and experimental study of external synchronization of two-frequency oscillations

V. S. Anishchenko, S. V. Astakhov, T. E. Vadivasova, A. V. Feoktistov

International Research Institute of Nonlinear Dynamics, Saratov State University

Abstract: The effect of synchonization has been studied in a system of two coupled Van der Pol oscillators under external harmonic force. The bifurcation analysis has been carried out using the phase approach. The mechanisms of complete and partial synchronization have been established. The main type of bifurcation described in the paper is the saddle-node bifurcation of invariant curves that corresponds to the saddle-node bifurcation of two-dimensional tori in the complete system of differential equations for the dynamical system under study. We illustrate the bifurcational mechanisms obtained from numerical experiment by the results of physical experiment. The synchronization phenomenon in the vicinity of resonances on a torus with winding numbers $1:1$ and $1:3$ is considered in the physical experiment.

Keywords: limit cycle, torus, saddle-node bifurcation, synchronization.

Full text: PDF file (1357 kB)
UDC: 517.9
MSC: 39Axx, 93D05
Received: 10.03.2009

Citation: V. S. Anishchenko, S. V. Astakhov, T. E. Vadivasova, A. V. Feoktistov, “Numerical and experimental study of external synchronization of two-frequency oscillations”, Nelin. Dinam., 5:2 (2009), 237–252

Citation in format AMSBIB
\Bibitem{AniAstVad09}
\by V.~S.~Anishchenko, S.~V.~Astakhov, T.~E.~Vadivasova, A.~V.~Feoktistov
\paper Numerical and experimental study of external synchronization of two-frequency oscillations
\jour Nelin. Dinam.
\yr 2009
\vol 5
\issue 2
\pages 237--252
\mathnet{http://mi.mathnet.ru/nd91}


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    This publication is cited in the following articles:
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    2. Kuznetsov A.P., Kuznetsov S.P., Stankevich N.V., “Avtonomnyi generator kvaziperiodicheskikh kolebanii”, Izv. vuzov. Prikladnaya nelineinaya dinamika, 18:2 (2010), 51–61  zmath  elib
    3. Kuznetsov A.P., Sataev I.R., Tyuryukina L.V., “Na puti k mnogomernym toram”, Izv. vuzov. Prikladnaya nelineinaya dinamika, 18:6 (2010), 65–84  zmath  elib
    4. Kuznetsov A.P., Sataev I.R., Tyuryukina L.V., “Synchronization of quasi-periodic oscillations in coupled phase oscillators”, Technical Physics Letters, 36:5 (2010), 478–481  crossref  adsnasa  isi  elib  scopus
    5. A. P. Kuznetsov, I. R. Sataev, L. V. Tyuryukina, “Sinkhronizatsiya i mnogochastotnye kolebaniya v tsepochke fazovykh ostsillyatorov”, Nelineinaya dinam., 6:4 (2010), 693–717  mathnet
    6. 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
    7. Peregorodova E.N., Ryskin N.M., Usacheva S.A., “Sinkhronizatsiya sistemy dvukh konkuriruyuschikh mod vneshnim garmonicheskim signalom”, Izvestiya vysshikh uchebnykh zavedenii. Prikladnaya nelineinaya dinamika, 19:3 (2011), 154–170  zmath  elib
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    10. 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
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    13. Emelianova Yu.P., Kuznetsov A.P., Sataev I.R., Turukina L.V., “Synchronization and Multi-Frequency Oscillations in the Low-Dimensional Chain of the Self-Oscillators”, Phys. D, 244:1 (2013), 36–49  crossref  zmath  adsnasa  isi  elib  scopus
    14. 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
    15. K. Kamiyama, N. Inaba, M. Sekikawa, T. Endo, “Bifurcation boundaries of three-frequency quasi-periodic oscillations in discrete-time dynamical system”, Phys. D, 289 (2014), 12–17  crossref  mathscinet  zmath  isi  elib  scopus
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    21. Sekikawa M. Inaba N., “A Complete Bifurcation Set of Chenciner Bubbles”, IEICE Trans. Fundam. Electron. Commun. Comput. Sci., E98A:12 (2015), 2719–2722  crossref  isi
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