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Optimal phase description of chaotic oscillators

Justus T. C. Schwabedal1,2,*, Arkady Pikovsky2, Björn Kralemann3, and Michael Rosenblum2

  • 1Department of Physiology, Marburg University, D-35037 Marburg, Germany
  • 2Department of Physics and Astronomy, Potsdam University, D-14476 Potsdam, Germany
  • 3Department of Education Science, Christian-Albrechts-University Kiel, D-24118 Kiel, Germany

  • *jschwabedal@googlemail.com
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Phys. Rev. E 85, 026216 – Published 27 February, 2012

DOI: https://doi.org/10.1103/PhysRevE.85.026216

Abstract

We introduce an optimal phase description of chaotic oscillations by generalizing the concept of isochrones. On chaotic attractors possessing a general phase description, we define the optimal isophases as Poincaré surfaces showing return times as constant as possible. The dynamics of the resultant optimal phase is maximally decoupled from the amplitude dynamics and provides a proper description of the phase response of chaotic oscillations. The method is illustrated with the Rössler and Lorenz systems.

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Outline

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Phys. Rev. E 85, 026216– Published 27 February, 2012
  • Received 19 October 2011

©2012 American Physical Society

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