Detecting couplings between interacting oscillators with time-varying basic frequencies: Instantaneous wavelet bispectrum and information theoretic approach

Janez Jamšek, Milan Paluš, and Aneta Stefanovska
Phys. Rev. E 81, 036207 – Published 5 March 2010

Abstract

In the natural world, the properties of interacting oscillatory systems are not constant, but evolve or fluctuating continuously in time. Thus, the basic frequencies of the interacting oscillators are time varying, which makes the system analysis complex. For studying their interactions we propose a complementary approach combining wavelet bispectral analysis and information theory. We show how these methods uncover the interacting properties and reveal the nature, strength, and direction of coupling. Wavelet bispectral analysis is generalized as a technique for detecting instantaneous phase-time dependence for the case of two or more coupled nonlinear oscillators whereas the information theory approach can uncover the directionality of coupling and extract driver-response relationships in complex systems. We generate bivariate time-series numerically to mimic typical situations that occur in real measured data, apply both methods to the same time-series and discuss the results. The approach is applicable quite generally to any system of coupled nonlinear oscillators.

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  • Received 31 October 2009

DOI:https://doi.org/10.1103/PhysRevE.81.036207

©2010 American Physical Society

Authors & Affiliations

Janez Jamšek1,2,3, Milan Paluš4, and Aneta Stefanovska1,3

  • 1Nonlinear Dynamics and Synergetics Group, Faculty of Electrical Engineering, University of Ljubljana, Ljubljana, Slovenia
  • 2Department of Physics and Technical Studies, Faculty of Education, University of Ljubljana, Ljubljana, Slovenia
  • 3Department of Physics, Lancaster University, Lancaster, United Kingdom
  • 4Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague, Czech Republic

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Vol. 81, Iss. 3 — March 2010

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