TY - JOUR

T1 - Detecting couplings between interacting oscillators with time-varying basic frequencies: Instantaneous wavelet bispectrum and information theoretic approach

AU - Jamsek, Janez

AU - Palus, Milan

AU - Stefanovska, Aneta

N1 - © 2010 The American Physical Society

PY - 2010/3/5

Y1 - 2010/3/5

N2 - 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.

AB - 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.

U2 - 10.1103/PhysRevE.81.036207

DO - 10.1103/PhysRevE.81.036207

M3 - Journal article

VL - 81

JO - Physical Review E

JF - Physical Review E

SN - 1539-3755

IS - 3

M1 - 036207

ER -