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    Nikita Ryskin

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


    Balakin M. I., Ryskin N. M.
    The mechanism of formation of multistability in a van der Pol generator with time-delayed feedback is studied. It is found that the developed multistability is formed through a sequence of two types of bifurcations: supercritical Andronov–Hopf bifurcation and subcritical Neimark–Sacker bifurcation. With variation of the control parameters, the fixed point repeatedly undergoes supercritical Andronov–Hopf bifurcation, which leads to an increase in the number of saddle cycles. The limit cycles acquire stability after a number of subcritical Neimark– Sacker bifurcations. The dynamics of the system is studied in a wide range of control parameters values.
    Keywords: Time delay, bifurcations, multistability
    Citation: Balakin M. I., Ryskin N. M.,  Bifurcational mechanism of formation of developed multistability in a van der Pol oscillator with time-delayed feedback, Rus. J. Nonlin. Dyn., 2017, Vol. 13, No. 2, pp.  151-164
    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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