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Kuznetsov A. P., Sataev I. R., Turukina L. V. On the way towards multidimensional tori. Izvestiya VUZ. Applied Nonlinear Dynamics, 2010, vol. 18, iss. 6, pp. 65-84. DOI: 10.18500/0869-6632-2010-18-6-65-84

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On the way towards multidimensional tori

Kuznetsov Aleksandr Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Sataev Igor Rustamovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Turukina L. V., Saratov State University

The problem of the dynamics of three coupled self-oscillators and three coupled periodically driven self-oscillators is discussed, in the last case only one of the oscillators is directly exited by the external fore. The regions of complete synchronization, two-, threeand four-frequency tori and chaos are revealed. Three typical situations of synchronization of three self-oscillators by the external driving are found. First situation refers to the mode locking of autonomous oscillators. Two other situations refer to quasi-periodic dynamics in the coupled autonomous oscillators. It is shown that multi-dimensional tori are not replaced by chaos and may dominate in the latter two cases. For the non-autonomous system under consideration the types of dynamics of three coupled oscillators are found, for which the complete synchronization of the system by the external driving is impossible independently of signal’s amplitude and frequency.

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