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2013
Impact Factor

    Kirill Morozov

    603950, Russia, Nizhny Novgorod, Gagarin Ave., 23
    Lobachevsky State University of Nizhny Novgorod

    Publications:

    Morozov A. D., Morozov K. E.
    On Synchronization of Quasiperiodic Oscillations
    2018, Vol. 14, no. 3, pp.  367-376
    Abstract
    We study the role of quasi-periodic perturbations in systems close to two-dimensional Hamiltonian ones. Similarly to the problem of the influence of periodic perturbations on a limit cycle, we consider the problem of the passage of an invariant torus through a resonance zone. The conditions for synchronization of quasi-periodic oscillations are established. We illustrate our results using the Duffing –Van der Pol equation as an example.
    Keywords: resonances, quasi-periodic, periodic, synchronization, averaged system, phase curves, equilibrium states
    Citation: Morozov A. D., Morozov K. E.,  On Synchronization of Quasiperiodic Oscillations, Rus. J. Nonlin. Dyn., 2018, Vol. 14, no. 3, pp.  367-376
    DOI:10.20537/nd180307
    Morozov K. E.
    Transitory Shift in the FitzHugh – Nagumo Model
    2018, Vol. 14, no. 2, pp.  169-177
    Abstract
    A nonautonomous analogue of the FitzHugh–Nagumo model is considered. It is supposed that the system is transitory, i.e., it is autonomous except on some compact interval of time. We first study the past and future vector fields that determine the system outside the interval of time dependence. Then we build the transition map numerically and discuss the influence of the transitory shift on the solutions behavior.
    Keywords: FitzHugh – Nagumo model, transitory system, separatrix, limit cycles, attractors
    Citation: Morozov K. E.,  Transitory Shift in the FitzHugh – Nagumo Model, Rus. J. Nonlin. Dyn., 2018, Vol. 14, no. 2, pp.  169-177
    DOI:10.20537/nd180202
    Morozov A. D., Morozov K. E.
    Transitory shift in pendular type equations
    2016, Vol. 12, No. 4, pp.  577–589
    Abstract
    The two-dimensional nonautonomous equations of pendular type are considered: the Josephson equation and the equation of oscillations of a body. It is supposed that these equations are transitory, i.e., nonautonomous only on a finite time interval. The problem of dependence of the mode on the transitory shift is solved. For a conservative case the measure of transport from oscillations to rotations is established.
    Keywords: transitory system, separatrix, limit cycles, attractors
    Citation: Morozov A. D., Morozov K. E.,  Transitory shift in pendular type equations, Rus. J. Nonlin. Dyn., 2016, Vol. 12, No. 4, pp.  577–589
    DOI:10.20537/nd1604003
    Morozov A. D., Morozov K. E.
    Transitory shift in the flutter problem
    2015, Vol. 11, No. 3, pp.  447-457
    Abstract
    We consider the two-dimensional system, which occurs in the flutter problem. We assume that this system is transitory (one whose time-dependence is confined to a compact interval). In the conservative case of this problem, we identified measure of transport between the cells filled with closed trajectories. In the nonconservative case, we consider the impact of transitory shift to setting of one or another attractor. We give probabilities of changing a mode (stationary to auto-oscillation).
    Keywords: transitory system, separatrix, limit cycles, attractors, flutter
    Citation: Morozov A. D., Morozov K. E.,  Transitory shift in the flutter problem, Rus. J. Nonlin. Dyn., 2015, Vol. 11, No. 3, pp.  447-457
    DOI:10.20537/nd1503001

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