Kirill Morozov
603950, Russia, Nizhny Novgorod, Gagarin Ave., 23
Lobachevsky State University of Nizhny Novgorod
Publications:
Morozov A. D., Morozov K. E.
On QuasiPeriodic Parametric Perturbations of Hamiltonian Systems
2020, Vol. 16, no. 2, pp. 369378
Abstract
We study nonconservative quasiperiodic $m$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 quasiperiodic 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.

Morozov A. D., Morozov K. E.
Global Dynamics of Systems Close to Hamiltonian Ones Under Nonconservative Quasiperiodic Perturbation
2019, Vol. 15, no. 2, pp. 187198
Abstract
We study quasiperiodic nonconservative perturbations of twodimensional 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.

Morozov A. D., Morozov K. E.
On Synchronization of Quasiperiodic Oscillations
2018, Vol. 14, no. 3, pp. 367376
Abstract
We study the role of quasiperiodic perturbations in systems close to twodimensional 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 quasiperiodic oscillations are established. We illustrate our results
using the Duffing –Van der Pol equation as an example.

Morozov K. E.
Transitory Shift in the FitzHugh – Nagumo Model
2018, Vol. 14, no. 2, pp. 169177
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.

Morozov A. D., Morozov K. E.
Transitory shift in pendular type equations
2016, Vol. 12, No. 4, pp. 577–589
Abstract
The twodimensional 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.

Morozov A. D., Morozov K. E.
Transitory shift in the flutter problem
2015, Vol. 11, No. 3, pp. 447457
Abstract
We consider the twodimensional system, which occurs in the flutter problem. We assume that this system is transitory (one whose timedependence 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 autooscillation).
