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Regul. Chaotic Dyn., 2016, Volume 21, Issue 2, Pages 147–159 (Mi rcd71)  

This article is cited in 1 scientific paper (total in 1 paper)

Nonstationary Energy Localization vs Conventional Stationary Localization in Weakly Coupled Nonlinear Oscillators

Leonid I. Manevitcha, Agnessa Kovalevab, Grigori Sigalovc

a Institute of Chemical Physics, Russian Academy of Sciences, ul. Kosygina 4, Moscow, 119991, Russia
b Space Research Institute, Russian Academy of Sciences, ul. Profsoyuznaya 84/32, Moscow, 117997, Russia
c University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

Abstract: In this paper we study the effect of nonstationary energy localization in a nonlinear conservative resonant system of two weakly coupled oscillators. This effect is alternative to the well-known stationary energy localization associated with the existence of localized normal modes and resulting from a local topological transformation of the phase portraits of the system. In this work we show that nonstationary energy localization results from a global transformation of the phase portrait. A key to solving the problem is the introduction of the concept of limiting phase trajectories (LPTs) corresponding to maximum possible energy exchange between the oscillators. We present two scenarios of nonstationary energy localization under the condition of 1:1 resonance. It is demonstrated that the conditions of nonstationary localization determine the conditions of efficient targeted energy transfer in a generating dynamical system. A possible extension to multi-particle systems is briefly discussed.

Keywords: nonlinear oscillations, coupled oscillators, nonlinear resonances, systems with slow and fast motions

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00284
Russian Academy of Sciences - Federal Agency for Scientific Organizations OChN-1
OFN-15
This work was supported in part by the Russian Foundation for Basic Research (grant 14-01-00284). The work of L.I.M. and A.K. was also partially supported by the Russian Academy of Science (OChN-1, OFN-15).


DOI: https://doi.org/10.1134/S1560354716020015

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Bibliographic databases:

MSC: 34C15, 70K30, 70K70
Received: 11.04.2015
Accepted:10.10.2015
Language:

Citation: Leonid I. Manevitch, Agnessa Kovaleva, Grigori Sigalov, “Nonstationary Energy Localization vs Conventional Stationary Localization in Weakly Coupled Nonlinear Oscillators”, Regul. Chaotic Dyn., 21:2 (2016), 147–159

Citation in format AMSBIB
\Bibitem{ManKovSig16}
\by Leonid I. Manevitch, Agnessa Kovaleva, Grigori Sigalov
\paper Nonstationary Energy Localization vs Conventional Stationary Localization in Weakly Coupled Nonlinear Oscillators
\jour Regul. Chaotic Dyn.
\yr 2016
\vol 21
\issue 2
\pages 147--159
\mathnet{http://mi.mathnet.ru/rcd71}
\crossref{https://doi.org/10.1134/S1560354716020015}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3486002}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84963751625}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. O. V. Gendelman, T. P. Sapsis, “Energy exchange and localization in essentially nonlinear oscillatory systems: canonical formalism”, J. Appl. Mech.-Trans. ASME, 84:1 (2017), 011009  crossref  isi  scopus
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