World Academy of Science, Engineering and Technology
Published April 29, 2011 | Version 3238
Journal article Open

Revealing Nonlinear Couplings between Oscillators from Time Series

Description

Quantitative characterization of nonlinear directional couplings between stochastic oscillators from data is considered. We suggest coupling characteristics readily interpreted from a physical viewpoint and their estimators. An expression for a statistical significance level is derived analytically that allows reliable coupling detection from a relatively short time series. Performance of the technique is demonstrated in numerical experiments.

Files

3238.pdf

Files (127.4 kB)

Name Size
md5:ffa63483fe856aca5abcf26954a89db5
127.4 kB Preview Download

Additional details

References

  • A. Pikovsky, M. Rosenblum, J. Kurths, Synchronization. A Universal Concept in Nonlinear Sciences (Cambridge Univ. Press, Cambridge, 2001).
  • M.G. Rosenblum, A.S. Pikovsky, Detecting direction of coupling in interacting oscillators, Phys. Rev. E 64 (2001) 045202(R).
  • D.A. Smirnov, B.P. Bezruchko, Estimation of interaction strength and direction from short and noisy time series, Phys. Rev. E 68 (2003) 046209.
  • B. Bezruchko et al, Characterizing direction of coupling from experimental observations}, Chaos 13 (2003) 179.
  • M. Palus, A. Stefanovska, Direction of coupling from phases of interacting oscillators: An information-theoretic approach, Phys. Rev. E 67 (2003) 055201(R).
  • K. Hlavackova-Schindler et al, Causality detection based on information-theoretic approaches in time series analysis, Phys. Rep. 441 (2007) 1.
  • M.G. Rosenblum et al, Identification of coupling direction: Application to cardiorespiratory interaction, Phys. Rev. E 65 (2002) 041909.
  • E. Pereda, R. Quian Quiroga, J. Bhattacharya, Nonlinear multivariate analysis of neurophysiological signals, Progr. Neurobiol. 77 (2005) 1.
  • J. Brea, D.F. Russell, A.B. Neiman, Measuring direction in the coupling of biological:a case study for electroreceptors of paddlefish, Chaos 16 (2006) 026111. [10] D. Smirnov et al, The generation of Parkinsonian tremor as revealed by directional coupling analysis, Europhys. Lett. 83 (2008) 20003. [11] I.I. Mokhov, D.A. Smirnov, El Nino Southern Oscillation drives North Atlantic Oscillation as revealed with nonlinear techniques from climatic indices, Geophys. Res. Lett. 33 (2006) L03708. [12] A.S. Pikovsky, M.G. Rosenblum, J. Kurths, Phase synchronization in regular and chaotic systems, Int. J. Bif. Chaos 10 (2000) 2291. [13] D.A. Smirnov, B.P. Bezruchko, Detection of couplings in ensembles of stochastic oscillators, Phys. Rev. E 79 (2009) 046204.