ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Kuznetsov A. P., Turukina L. V. Subharmonic resonance in a system of two dissipative coupled van der Pol oscillators with external force. Izvestiya VUZ. Applied Nonlinear Dynamics, 2013, vol. 21, iss. 5, pp. 69-78. DOI: 10.18500/0869-6632-2013-21-5-69-78

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Subharmonic resonance in a system of two dissipative coupled van der Pol oscillators with external force

Kuznetsov Aleksandr Petrovich, 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 excitation of two coupled oscillators is discussed in the case of the simple subharmonic resonance between the external force and eigen-frequencies of the oscillators. The corresponded phase equation is obtained. We showed that the form of the synchronization tongue and transformation of the region of the two-, three-frequency tori by varying the parameter of the coupling between the oscillators is significantly different from the case of the main resonance. We illustrated the efficiency of the phase model by the comparison of Lyapunov’s charts plotted for the case of the original system and for the phase model.

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