Abstract
The phenomenon of synchronization of two oscillators under the action of an external force has been studied in a phase approximation. The Lyapunov maps are presented and the possible types of regimes are considered. Various types of two-frequency tori are revealed and classified.
Similar content being viewed by others
References
P. S. Landa, Nonlinear Oscillations and Waves in Dynamical Systems (Kluwer Academic Publishers, Dordrecht, 1996; Nauka, Moscow, 1997).
A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: Universal Concept in Nonlinear Sciences (Cambridge University Press, Cambridge, 2001).
A. P. Kuznetsov, S. P. Kuznetsov, and N. M. Ryskin, Nonlinear Oscillations (Fizmatlit, Moscow, 2002) [in Russian].
V. S. Anishchenko, S. V. Astakhov, T. E. Vadivasova, and G. I. Strelkova, Synchronization of Regular, Chaotic, and Stochastic Oscillations (Institute of Computer Investigations, Moscow-Izhevsk, 2008) [in Russian].
V. Anishchenko, S. Nikolaev, and J. Kurths, Chaos 18, 037123 (2008).
V. S. Anishchenko, S. V. Astakhov, and T. E. Vadivasova, Europhys. Lett. 86, 30 003 (2009).
V. S. Anishchenko, S. V. Astakhov, T. E. Vadivasova, and A. V. Feoktistov., Nelin. Dinam. 5, 237 (2009).
V. I. Arnol’d and Yu. S. Il’yashenko, Ordinary Differential Equations (Itogi Nauki Tekh.: Sovrem. Probl. Mat., Fundam. Napravl., Vol. 1) (VINITI, Moscow, 1985).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.P. Kuznetsov, I.R. Sataev, L.V. Tyuryukina, 2010, published in Pis’ma v Zhurnal Tekhnicheskoĭ Fiziki, 2010, Vol. 36, No. 10, pp. 73–80.
Rights and permissions
About this article
Cite this article
Kuznetsov, A.P., Sataev, I.R. & Tyuryukina, L.V. Synchronization of quasi-periodic oscillations in coupled phase oscillators. Tech. Phys. Lett. 36, 478–481 (2010). https://doi.org/10.1134/S1063785010050263
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063785010050263