Skip to main content
Log in

A data-analysis method for decomposing synchronization variability of anticipatory systems into stochastic and deterministic components

  • Statistical and Nonlinear Physics
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

Synchronization has been shown to be a valuable concept in the field of nonlinear dynamics and dynamical systems in general. Deviation from perfect synchronization results from an interplay of deterministic coupling forces and stochastic fluctuating forces. When the exact details of these two sources of variance are unknown, it becomes useful to estimate them directly from data. To this end, we develop a data analysis method for estimating parameters associated with these deterministic and stochastic components. The method relies on separating their respective contributions to synchronization error. We focus on the case where a slave system synchronizes with the future of a master system, so-called anticipating synchronization.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • A. Pikovsky, M. Rosenblum, J. Kurths, R. Hilborn, Synchronization: A Universal Concept in Nonlinear Science (Cambridge Univ. Press, 2003)

  • T. Sheridan, W. Ferrell, Man-machine systems: information, control, and decision models of human performance (MIT Press, 1974)

  • C. Wickens, Engineering psychology and human performance, 2nd edn. (Harper-Collins, New York, 1992)

  • A. Budini, M. Cáceres, Physica A 387, 4483 (2008)

    Google Scholar 

  • G.R. Jafari, S.M. Fazeli, F. Ghasemi, S.M.V. Allaei, M.R.R. Tabar, A.I. Zad, G. Kavei, Phys. Rev. Lett. 91, 226101 (2002)

    Google Scholar 

  • P. Sura, J. Barsugli, Phys. Lett. A 305, 304 (2002)

    Google Scholar 

  • M. Waechter, F. Riess, T. Schimmel, U. Wendt, J. Peinke, Eur. Phys. J. B 41, 259 (2004)

    Google Scholar 

  • T. Kuusela, Phys. Rev. E 69, 031916 (2004)

    Google Scholar 

  • T.D. Frank, P.J. Beek, R. Friedrich, Phys. Lett. A 328, 219 (2004)

    Google Scholar 

  • R. Friedrich, J. Peinke, Phys. Rev. Lett. 78, 863 (1997)

    Google Scholar 

  • J. Gradisek, R. Friedrich, E. Govekar, I. Grabec, Phys. Lett. A 294, 234 (2002)

    Google Scholar 

  • A. Wilmer, T.D. Frank, P.J. Beek, R. Friedrich, Eur. Phys. J. B 60, 203 (2007)

    Google Scholar 

  • H.U. Voss, Phys. Rev. E 61, 5115 (2000)

    Google Scholar 

  • H.U. Voss, Phys. Rev. Lett. 87, 014102 (2001)

    Google Scholar 

  • M. Ciszak, F. Marino, R. Toral, S. Balle, Phys. Rev. Lett. 93, 114102 (2004)

    Google Scholar 

  • S. Sivaprakasam, E.M. Shahverdiev, P.S. Spencer, K.A. Shore, Phys. Rev. Lett. 87, 154101 (2001)

    Google Scholar 

  • M.G. Rosenblum, A.S. Pikovsky, J. Kurths, Phys. Rev. Lett. 78, 4193 (1997)

    Google Scholar 

  • O. Rössler, Phys. Lett. A 57, 397 (1976)

    Google Scholar 

  • B. Kay, J. Kelso, E. Saltzman, G. Schöner, J. Experimental Psychology: Human Perception and Performance 13, 178 (1987)

    Google Scholar 

  • D. Mottet, R. Bootsma, Biol. Cybern. 80, 235 (1999)

    Google Scholar 

  • P. Silva, M. Moreno, M. Mancini, S. Fonseca, M.T. Turvey, Neurosci. Lett. 429, 64 (2007)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to N. Stepp.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Stepp, N., Frank, T. A data-analysis method for decomposing synchronization variability of anticipatory systems into stochastic and deterministic components. Eur. Phys. J. B 67, 251–257 (2009). https://doi.org/10.1140/epjb/e2009-00022-x

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjb/e2009-00022-x

PACS

Navigation