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    Yuliya Sedova

    Zelenaya 38, Saratov, 410019
    Institute of Radio Engineering and Electronics, Rassian Academy of Sciences, Saratov Branch


    Kuznetsov A. P., Kuznetsov S. P., Sedova Y. V.
    Examples of mechanical systems are discussed, where quasi-periodic motions may occur, caused by an irrational ratio of the radii of rotating elements that constitute the system. For the pendulum system with frictional transmission of rotation between the elements, in the conservative and dissipative cases we note the coexistence of an infinite number of stable fixed points, and in the case of the self-oscillating system the presence of many attractors in the form of limit cycles and of quasi-periodic rotational modes is observed. In the case of quasi-periodic dynamics the frequencies of spectral components depend on the parameters, but the ratio of basic incommensurate frequencies remains constant and is determined by the irrational number characterizing the relative size of the elements.
    Keywords: dynamic system, mechanical transmission, quasi-periodic oscillations, attractor
    Citation: Kuznetsov A. P., Kuznetsov S. P., Sedova Y. V.,  Pendulum system with an infinite number of equilibrium states and quasiperiodic dynamics, Rus. J. Nonlin. Dyn., 2016, Vol. 12, No. 2, pp.  223-234
    Kuznetsov A. P., Migunova N. A., Sataev I. R., Sedova Y. V., Turukina L. V.
    Ensembles of several chaotic R¨ossler oscillators are considered. It is shown that a typical phenomenon for such systems is the emergence of invariant tori of different and sufficiently high dimension. The possibility of a quasi-periodic Hopf bifurcation and of the cascade of such bifurcations based on tori of increasing dimension is demonstrated. The domains of resonant tori are revealed whose boundaries correspond to a saddle-node bifurcation. Within areas of resonant modes the torus-doubling bifurcations and tori destruction are observed.
    Keywords: chaos, quasiperiodic oscillations, invariant tori, Lyapunov exponents, bifurcations
    Citation: Kuznetsov A. P., Migunova N. A., Sataev I. R., Sedova Y. V., Turukina L. V.,  Dynamics of coupled chaotic oscillators: from chaos to quasiperiodicity, Rus. J. Nonlin. Dyn., 2014, Vol. 10, No. 4, pp.  387-405
    Dementyeva I. S., Kuznetsov A. P., Savin A. V., Sedova Y. V.
    Quasiperiodic dynamics of three coupled logistic maps
    2014, Vol. 10, No. 2, pp.  139-148
    The model of three linear-coupled logistic maps is examined. The structure of parameter plane (coupling value—period-doubling parameter) is discussed. We select configuration of coupling and parameters so, that regimes of three-frequency quasiperiodicity become possible. Also we consider bifurcations associated with such states.
    Keywords: quasiperiodic oscillations, invariant tori, bifurcations
    Citation: Dementyeva I. S., Kuznetsov A. P., Savin A. V., Sedova Y. V.,  Quasiperiodic dynamics of three coupled logistic maps, Rus. J. Nonlin. Dyn., 2014, Vol. 10, No. 2, pp.  139-148
    Kuznetsov S. P., Jalnine A. Y., Sataev I. R., Sedova Y. V.
    We perform a numerical study of the motion of the rattleback, a rigid body with a convex surface on a rough horizontal plane in dependence on the parameters, applying the methods used previously for the treatment of dissipative dynamical systems, and adapted for the nonholonomic model. Charts of dynamical regimes are presented on the parameter plane of the total mechanical energy and the angle between the geometric and dynamic principal axes of the rigid body. Presence of characteristic structures in the parameter space, previously observed only for dissipative systems, is demonstrated. A method of calculating for the full spectrum of Lyapunov exponents is developed and implemented. It is shown that analysis of the Lyapunov exponents of chaotic regimes of the nonholonomic model reveals two classes, one of which is typical for relatively high energies, and the second for the relatively small energies. For the model reduced to a three-dimensional map, the first one corresponds to a strange attractor with one positive and two negative Lyapunov exponents, and the second to the chaotic dynamics of the quasiconservative type, with close in magnitude positive and negative Lyapunov exponents, and the rest one about zero. The transition to chaos through a sequence of period-doubling bifurcations is illustrated, and the observed scaling corresponds to that intrinsic to the dissipative systems. A study of strange attractors is provided, in particularly, phase portraits are presented as well as the Lyapunov exponents, the Fourier spectra, the results of calculating the fractal dimensions.
    Keywords: rattleback, rigid body dynamics, nonholonomic mechanics, strange attractor, Lyapunov exponents, bifurcation, fractal dimension
    Citation: Kuznetsov S. P., Jalnine A. Y., Sataev I. R., Sedova Y. V.,  Phenomena of nonlinear dynamics of dissipative systems in nonholonomic mechanics of the rattleback, Rus. J. Nonlin. Dyn., 2012, Vol. 8, No. 4, pp.  735-762
    Kuznetsov A. P., Kuznetsov S. P., Pozdnyakov M. V., Sedova Y. V.
    We suggest a simple two-dimensional map, parameters of which are the trace and Jacobian of the perturbation matrix of the fixed point. On the parameters plane it demonstrates the main universal bifurcation scenarios: the threshold to chaos via period-doublings, the situation of quasiperiodic oscillations and Arnold tongues. We demonstrate the possibility of implementation of such map in radiophysical device.
    Keywords: maps, bifurcations, phenomena of quasiperiodicity
    Citation: Kuznetsov A. P., Kuznetsov S. P., Pozdnyakov M. V., Sedova Y. V.,  Universal two-dimensional map and its radiophysical realization, Rus. J. Nonlin. Dyn., 2012, Vol. 8, No. 3, pp.  461-471
    Kuznetsov A. P., Pozdnyakov M. V., Sedova Y. V.
    We examine the dynamics of the coupled system consisting of subsystems, demonstrating the Neimark–Sacker bifurcation. The study of coupled maps on the plane of the parameters responsible for such bifurcation in the individual subsystems is realized. On the plane of parameters characterizing the rotation numbers of the individual subsystems we reveal the complex structures consisting of the quasi-periodic modes of different dimensions and the exact periodic resonances of different orders.
    Keywords: maps, bifurcations, phenomena of quasiperiodicity
    Citation: Kuznetsov A. P., Pozdnyakov M. V., Sedova Y. V.,  Coupled universal maps demonstrating Neimark–Saker bifurcation, Rus. J. Nonlin. Dyn., 2012, Vol. 8, No. 3, pp.  473-482
    Kuznetsov A. P., Kuznetsov S. P., Sataev I. R., Sedova Y. V.
    In paper we suggest an example of system which dynamics is answered to conception of a «critical quasi-attractor». Besides the brief review of earlier obtained results the new results are presented, namely the illustrations of scaling for basins of attraction of elements of critical quasi-attractor, the renormalization group approach in the presence of additive uncorrelated noise, the calculation of universal constant responsible for the scaling regularities of the noise effect, the illustrations of transitions initialized by noise that are realized between coexisted attractors.
    Keywords: quasi-attractor, renormalization group method, type of criticality, bifurcation, scaling, noise
    Citation: Kuznetsov A. P., Kuznetsov S. P., Sataev I. R., Sedova Y. V.,  Critical point of accumulation of fold-flip bifurcation points and critical quasi-attractor (the review and new results), Rus. J. Nonlin. Dyn., 2008, Vol. 4, No. 2, pp.  113-132

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