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    Svetlana Gerasimova

    Astrahanskaya st. 83, Saratov, 410026, Russia
    Saratov State University named after N. G. Chernyshevsky


    Adilova A. B., Gerasimova S. A., Ryskin N. M.
    In this paper, mutual synchronization of two limit-cycle oscillators coupled with delay is studied. The results of bifurcation analysis are presented under the assumption that the delay is small in comparison with the oscillation build-up time. The stability conditions for in-phase and anti-phase modes of synchronization are analyzed at different values of parameters. The synchronization tongues on the frequency mismatch — coupling strength plane are presented.
    Keywords: bifurcation, delay, coupled oscillators, synchronization
    Citation: Adilova A. B., Gerasimova S. A., Ryskin N. M.,  Bifurcation analysis of mutual synchronization of two oscillators coupled with delay, Rus. J. Nonlin. Dyn., 2017, Vol. 13, No. 1, pp.  3-12
    Peregorodova E. N., Gerasimova S. A., Ryskin N. M.
    Forced synchronization of a simple model of a three-mode self-oscillator which demonstrates appearance of self-modulation is considered. External driving at the fundamental frequency as well as at the self-modulation satellite frequency is considered. Structures of synchronization domains on the driving frequency — driving amplitude parameter plane and mechanisms of transition to the synchronous regime are investigated for the cases of single-mode and selfmodulated operation of the free-running oscillator.
    Keywords: nonlinear oscillations, automodulation, synchronization, mode competition
    Citation: Peregorodova E. N., Gerasimova S. A., Ryskin N. M.,  On the theory of forced synchronization of self-modulated oscillations, Rus. J. Nonlin. Dyn., 2012, Vol. 8, No. 5, pp.  913-929

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