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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 Quasi-Periodic Parametric Perturbations of Hamiltonian Systems 2020, Vol. 16, no. 2, pp.  369-378 Abstract We study nonconservative quasi-periodic $m$-frequency $\it parametric$ perturbations of twodimensional nonlinear Hamiltonian systems. Our objective is to specify the conditions for the existence of new regimes in resonance zones, which may arise due to parametric terms in the perturbation. These regimes correspond to $(m + 1)$-frequency quasi-periodic solutions, which are not generated from Kolmogorov tori of the unperturbed system. The conditions for the existence of these solutions are found. The study is based on averaging theory and the analysis of the corresponding averaged systems. We illustrate the results with an example of a Duffing type equation. Keywords: resonances, quasi-periodic, parametric, averaging method, limit cycles, invariant torus, phase curves, equilibrium states Citation: Morozov A. D., Morozov K. E.,  On Quasi-Periodic Parametric Perturbations of Hamiltonian Systems, Rus. J. Nonlin. Dyn., 2020, Vol. 16, no. 2, pp.  369-378 DOI:10.20537/nd200210
 Morozov A. D., Morozov K. E. Global Dynamics of Systems Close to Hamiltonian Ones Under Nonconservative Quasi-periodic Perturbation 2019, Vol. 15, no. 2, pp.  187-198 Abstract We study quasi-periodic nonconservative perturbations of two-dimensional Hamiltonian systems. We suppose that there exists a region $D$ filled with closed phase curves of the unperturbed system and consider the problem of global dynamics in $D$. The investigation includes examining the behavior of solutions both in $D$ (the existence of invariant tori, the finiteness of the set of splittable energy levels) and in a neighborhood of the unperturbed separatrix (splitting of the separatrix manifolds). The conditions for the existence of homoclinic solutions are stated. We illustrate the research with the Duffing – Van der Pole equation as an example. Keywords: resonances, quasi-periodic, periodic, averaged system, phase curves, equilibrium states, limit cycles, separatrix manifolds Citation: Morozov A. D., Morozov K. E.,  Global Dynamics of Systems Close to Hamiltonian Ones Under Nonconservative Quasi-periodic Perturbation, Rus. J. Nonlin. Dyn., 2019, Vol. 15, no. 2, pp.  187-198 DOI:10.20537/nd190208
 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