Regular and Chaotic Dynamics

, Volume 21, Issue 2, pp 147–159 | Cite as

Nonstationary energy localization vs conventional stationary localization in weakly coupled nonlinear oscillators

  • Leonid I. Manevitch
  • Agnessa Kovaleva
  • Grigori Sigalov
Article
  • 69 Downloads

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 

MSC2010 numbers

34C15 70K30 70K70 

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Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  • Leonid I. Manevitch
    • 1
  • Agnessa Kovaleva
    • 2
  • Grigori Sigalov
    • 3
  1. 1.Institute of Chemical PhysicsRussian Academy of SciencesMoscowRussia
  2. 2.Space Research InstituteRussian Academy of SciencesMoscowRussia
  3. 3.University of Illinois at Urbana-ChampaignUrbanaUSA

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