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Nelin. Dinam., 2018, Volume 14, Number 3, Pages 367–376 (Mi nd619)  

On Synchronization of Quasiperiodic Oscillations

A. D. Morozov, K. E. Morozov

Lobachevsky State University of Nizhny Novgorod, prosp. Gagarina 23, Nizhny Novgorod, 603950, Russia

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

Funding Agency Grant Number
Russian Foundation for Basic Research 18-01-00306
16-01-00364
Russian Science Foundation 14-41-00044
Ministry of Education and Science of the Russian Federation 1.3287.2017/PCh
This work was supported by the Russian Foundation for Basic Research under grants nos. 18-01-00306, 16-01-00364 and by the Russian Science Foundation under grant no. 14-41-00044, by the Ministry of Education and Science of the Russian Federation (project no. 1.3287.2017/PCh).


DOI: https://doi.org/10.20537/nd180307

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MSC: 34C15
Received: 11.05.2018
Accepted:22.06.2018
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Citation: A. D. Morozov, K. E. Morozov, “On Synchronization of Quasiperiodic Oscillations”, Nelin. Dinam., 14:3 (2018), 367–376

Citation in format AMSBIB
\Bibitem{MorMor18}
\by A. D. Morozov, K. E. Morozov
\paper On Synchronization of Quasiperiodic Oscillations
\jour Nelin. Dinam.
\yr 2018
\vol 14
\issue 3
\pages 367--376
\mathnet{http://mi.mathnet.ru/nd619}
\crossref{https://doi.org/10.20537/nd180307}
\elib{http://elibrary.ru/item.asp?id=36296376}


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