A. A. Karabanov, A. D. Morozov, “To the theory of coupled oscillations passing through the resonance”, Regul. Chaotic Dyn., 2006, Volume 11, Issue 2,Pages <nobr>259

On the 70th birthday of L.P. Shilnikov

To the theory of coupled oscillations passing through the resonance

A. A. Karabanov^a, A. D. Morozov^b

^a Department of Mathematics, Komi Science Center, Ural Division of RAS, 3a Chernov Street, Syktyvkar 167982, Komi, Russia
^b Department of Mathematics and Mechanics, Nizhny Novgorod State University, 603950 Nizhny Novgorod, Russia

Abstract: 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.

Keywords: near-integrable systems, coupled oscillations, resonances, self-synchronization.

MSC: 34C15, 34C28, 37G35, 70K30

Received: 26.07.2005
Accepted: 15.11.2005

Language: English

DOI: 10.1070/RD2006v011n02ABEH000349