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Detection of weak directional coupling: Phase-dynamics approach versus state-space approach Dmitry A. Smirnov
 

Summary: Detection of weak directional coupling: Phase-dynamics approach versus state-space approach
Dmitry A. Smirnov
Saratov Branch of Institute of RadioEngineering and Electronics of the Russian Academy of Sciences, 38 Zelyonaya Street,
Saratov 410019, Russia
Ralph G. Andrzejak
John von Neumann­Institute for Computing, Forschungszentrum Jülich, 52425 Jülich, Germany
Received 29 September 2004; published 15 March 2005
We compare two conceptually different approaches to the detection of weak directional couplings between
two oscillatory systems from bivariate time series. The first approach is based on the analysis of the systems'
phase dynamics, whereas the other one tests for interdependencies in the reconstructed state spaces of the
systems. We analyze the sensitivity of both techniques to weak couplings in numerical experiments by con-
sidering couplings between almost identical as well as between significantly different nonlinear systems. We
study different degrees of phase diffusion, test the robustness of the two techniques against observational noise,
and investigate the influence of the time series length. Our results show that none of the two approaches is
generally superior to the other, and we conclude that it is probably the combination of both techniques that
would allow the most comprehensive and reliable characterization of coupled systems.
DOI: 10.1103/PhysRevE.71.036207 PACS number s : 05.45.Tp, 05.45.Xt
I. INTRODUCTION
The complex interplay of dynamical systems results in a
rich variety of synchronization phenomena. While often the

  

Source: Andrzejak, Ralph Gregor - Departament de Tecnologia, Universitat Pompeu Fabra

 

Collections: Computer Technologies and Information Sciences