Select language: En
0
2013
Impact Factor

    Albert Morozov

    pr. Gagarina 23, Nizhny Novgorod, 603950 Russia
    N.I. Lobachevsky State University of Nizhny Novgorod

    Publications:

    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
    Afraimovich V. S., Belyakov L. A., Bykov V. V., Gonchenko S. V., Lerman L. M., Lukyanov V. I., Malkin M. I., Morozov A. D., Turaev D. V.
    Leonid Pavlovich Shilnikov (17.12.1934–26.12.2011)
    2012, Vol. 8, No. 1, pp.  183-186
    Abstract
    Citation: Afraimovich V. S., Belyakov L. A., Bykov V. V., Gonchenko S. V., Lerman L. M., Lukyanov V. I., Malkin M. I., Morozov A. D., Turaev D. V.,  Leonid Pavlovich Shilnikov (17.12.1934–26.12.2011), Rus. J. Nonlin. Dyn., 2012, Vol. 8, No. 1, pp.  183-186
    DOI:10.20537/nd1201015
    Kondrashov R. E., Morozov A. D.
    Abstract
    The problem of global behavior of solutions in system of two Duffing–Van der Pole equations close to nonlinear integrable is considered. For regions without unperturbed separatrixes we give partially averaged systems which describe the behavior of solutions of original system in resonant zones. The finiteness of number of non-trivial resonant structures is established. Also we give fully averaged systems which describe the behavior of solutions outside of neighborhoods of nontrivial resonant structures. The results of numerically investigation of these systems are resulted.
    Keywords: limit cycles, resonances, averaging
    Citation: Kondrashov R. E., Morozov A. D.,  On global behaviour of the solutions of system of two Duffing–Van der Pole equations, Rus. J. Nonlin. Dyn., 2011, Vol. 7, No. 3, pp.  437-449
    DOI:10.20537/nd1103003
    Kondrashov R. E., Morozov A. D.
    Abstract
    We consider a problem about interaction of the two Duffing—van der Pol equations close to nonlinear integrable. The average systems describing behaviour of the solutions of the initial equation in resonant zones are deduced. The conditions of existence of not trivial resonant structures are established. The results of research in cases are resulted, when at the uncoupled equations exist and there are no limiting cycles.
    Keywords: limit cycles, resonances
    Citation: Kondrashov R. E., Morozov A. D.,  On investigation of resonances in system of two Duffing–van der Pol equations, Rus. J. Nonlin. Dyn., 2010, Vol. 6, No. 2, pp.  241-254
    DOI:10.20537/nd1002001
    Korolev S. A., Morozov A. D.
    Abstract
    In this paper we consider time-periodic perturbations of self-oscillating pendulum equation which arises from analysis of one system with two degrees of freedom. We derive averaged systems which describe the behavior of solutions of original equation in resonant areas and we find existence condition of Poincare homoclinic structure. In the case when autonomous equation has 5 limit cycles in oscillating region we give results of numerical computation. Under variation of perturbation frequency we investigate bifurcations of phase portraits of Poincare map.
    Keywords: pendulum equation, limit cycles, resonances
    Citation: Korolev S. A., Morozov A. D.,  On periodic perturbations of self-oscillating pendulum equations, Rus. J. Nonlin. Dyn., 2010, Vol. 6, No. 1, pp.  79-89
    DOI:10.20537/nd1001006

    Back to the list