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Nelin. Dinam., 2008, Volume 4, Number 1, Pages 39–56 (Mi nd219)  

This article is cited in 14 scientific papers (total in 14 papers)

Synchronization mechanisms of resonant limit cycle on two-dimensional torus

V. S. Anishchenkoa, S. M. Nikolaeva, J. Kurthsb

a Saratov State University
b Group of Nonlinear Dynamics, Institute of Physics, University of Potsdam

Abstract: We investigate synchronization of a resonant limit cycle on a two dimensional torus by an external harmonic signal. The regime of resonant limit cycle is realized in a system of two coupled Van der Pol oscillators, we consider the resonances 1:1 and 1:3. We analyse the influence of the generators coupling strength. We show, that generally the effect of synchronization of a resonant limit cycle on torus is followed by the distruction of the resonance in the system, next one of the basic frequencies of the system becomes locked, and then another. We consider the bifurcation mechanism of synchronization effect.

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

Full text: PDF file (1106 kB)
MSC: 39Axx, 93D05
Received: 14.12.2007

Citation: V. S. Anishchenko, S. M. Nikolaev, J. Kurths, “Synchronization mechanisms of resonant limit cycle on two-dimensional torus”, Nelin. Dinam., 4:1 (2008), 39–56

Citation in format AMSBIB
\Bibitem{AniNikKur08}
\by V.~S.~Anishchenko, S.~M.~Nikolaev, J.~Kurths
\paper Synchronization mechanisms of resonant limit cycle on two-dimensional torus
\jour Nelin. Dinam.
\yr 2008
\vol 4
\issue 1
\pages 39--56
\mathnet{http://mi.mathnet.ru/nd219}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Anischenko V.S., Nikolaev S.M., “Sinkhronizatsiya kvaziperiodicheskikh kolebanii s dvumya chastotami”, Izv. vuzov. Prikladnaya nelineinaya dinamika, 16:2 (2008), 69–86  elib
    2. Kuznetsov A.P., Sataev I.R., Tyuryukina L.V., “Fazovaya dinamika vozbuzhdaemykh kvaziperiodicheskikh avtokolebatelnykh ostsillyatorov”, Izv. vuzov. Prikladnaya nelineinaya dinamika, 18:4 (2010), 17–32  zmath  elib
    3. 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
    4. 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
    5. 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
    6. 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
    7. A. P. Kuznetsov, N. V. Stankevich, “Sinkhronizatsiya generatorov kvaziperiodicheskikh kolebanii”, Nelineinaya dinam., 9:3 (2013), 409–419  mathnet
    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. Kamiyama K., Inaba N., Sekikawa M., Endo T., “Bifurcation Boundaries of Three-Frequency Quasi-Periodic Oscillations in Discrete-Time Dynamical System”, Physica D, 289 (2014), 12–17  crossref  isi
    10. 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
    11. Inaba N., Kamiyama K., Kousaka T., Endo T., “Numerical and Experimental Observation of Arnol'D Resonance Webs in An Electrical Circuit”, Physica D, 311 (2015), 17–24  crossref  isi
    12. Hidaka Sh., Inaba N., Sekikawa M., Endo T., “Bifurcation Analysis of Four-Frequency Quasi-Periodic Oscillations in a Three-Coupled Delayed Logistic Map”, Phys. Lett. A, 379:7 (2015), 664–668  crossref  isi
    13. Sekikawa M., Inaba N., “Doubly Twisted Neimark-Sacker Bifurcation and Two Coexisting Two-Dimensional Tori”, Phys. Lett. A, 380:1-2 (2016), 171–176  crossref  isi
    14. Tri Quoc Truong, Tsubone T., Sekikawa M., Inaba N., “Complicated Quasiperiodic Oscillations and Chaos From Driven Piecewise-Constant Circuit: Chenciner Bubbles Do Not Necessarily Occur Via Simple Phase-Locking”, Physica D, 341 (2017), 1–9  crossref  mathscinet  zmath  isi  scopus
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