167610, Cernova,3a, Syktyvkar
Department of Mathematics of Ural Division of RAS
Karabanov A. A., Morozov A. D.
To the theory of coupled oscillations passing through the resonance
2006, vol. 11, no. 2, pp. 259-268
The problem of coupled oscillations is considered in the case when a stable equilibrium of a globally averaged system passes through a resonance curve. Questions of persistence of invariant tori and transition to a self-synchronization are particularly discussed.
Karabanov A. A.
Resonances in Four-Dimensional Quasi-Hamiltonian Systems: Analysis and Simulations
2001, vol. 6, no. 1, pp. 17-32
The problem of qualitative behaviour of four-dimensional quasi-Hamiltonian system in a neighbourhood of a fixed resonance is considered. The general analytical grounds of the problem are touched upon. We turn to the global analysis of special three-dimensional system averaged near the resonance. Furthermore, a checking the theory against numerical simulations is made. Two physical examples, revealing an irregular resonant dynamics, are studied.