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Instantaneous frequencies of a chaotic system

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Abstract

The structure and geometry of high-dimensional, complex dynamical systems is usually hidden under a profusion of numerical data. We show that time-frequency analysis allows one to analyze these data regardless of the number of degrees of freedom. Our method takes snapshots of the system in terms of its instantaneous frequencies defined as ridges of the time-frequency landscape. Using the wavelet transform of a single trajectory, it can characterize key dynamical properties like the extent of chaos, resonance transitions and trappings.

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Authors and Affiliations

  1. Centre de Physique Théorique, CNRS Luminy, Case 907, F-13288, Marseille Cedex 9, France

    C. Chandré

  2. Center for Nonlinear Science, School of Physics, Georgia Institute of Technology, 30332-0430, Atlanta, Georgia, USA

    T. Uzer

Authors
  1. C. Chandré
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  2. T. Uzer
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Additional information

Unité Mixte de Recherche (UMR 6207) du CNRS, et des universités Aix-Marseille I, Aix-Marseille II et du Sud Toulon-Var. Laboratoire affilié à la FRUMAM (FR 2291).

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Chandré, C., Uzer, T. Instantaneous frequencies of a chaotic system. Pramana - J Phys 64, 371–379 (2005). https://doi.org/10.1007/BF02704564

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  • DOI: https://doi.org/10.1007/BF02704564

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