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Extending the HKB model of coordinated movement to oscillators with different eigenfrequencies

Biological Cybernetics volume 74, pages 21–30 (1996)Cite this article

Abstract

We study the dynamics of a system of coupled nonlinear oscillators that has been used to model coordinated human movement behavior. In contrast to earlier work we examine the case where the two component oscillators have different eigenfrequencies. Problems related to the decomposition of a time series (from an experiment) into amplitude and phase are discussed. We show that oscillations at multiples of the main frequency of the oscillator system may occur in the phase and amplitude due to the choice of a coordinate system and how these oscillations can be eliminated. We derive an explicit equation for the dynamics of the relative phase of the oscillator system in phase space that enables a direct comparison between theory and experiment.

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References

  • Bogoliubov NN, Mitropolsky YA (1961) Asymptotic methods in the theory of nonlinear oscillators. Hindustan Publishing Corporation, New Delhi

    Google Scholar 

  • Buchanan JJ, Kelso JAS (1993) Posturally induced transitions in rhythmic multijoint limb movements. Exp Brain Res 94:131–142

    Google Scholar 

  • Haken H (1983) Synergetics: an introduction, 3rd edn. Springer, Berlin Heidelberg New York

    Google Scholar 

  • Haken H (1987) Advanced synergetics, 2nd edn. Springer, Berlin Heidelberg New York

    Google Scholar 

  • Haken H (1991) Synergetic computers and cognition. Springer, Berlin Heidelberg New York

    Google Scholar 

  • Haken H, Kelso JAS, Bunz H (1985) A theoretical model of phase transitions in human hand movements. Biol Cybern 51:347–356

    Google Scholar 

  • Jeka JJ, Kelso JAS (in press) Manipulating symmetry in the coordination dynamics of human movement. J Exp Psychol Hum Percept Perform (in press)

  • Kay BA, Kelso JAS, Saltzman EL, Schöner GS (1987) The space-time behavior of single and bimanual movements: data and model. J Exp Psychol Hum Percept Perform 13:178–192

    Google Scholar 

  • Kelso JAS (1981) On the oscillatory basis of movement. Bull Psychonom Soc 18:63

    Google Scholar 

  • Kelso JAS (1984) Phase transitions and critical behavior in human bimanual coordination. Am J Physiol 15:R1000-R1004

    Google Scholar 

  • Kelso JAS, Jeka JJ (1992) Symmetry breaking dynamics of human multilimb coordination. J Exp Psychol Hum Percept Perform 18:645–668

    Google Scholar 

  • Kelso JAS, Kay BA (1987) Information and control: a macroscopic analysis of perception-action coupling. In: Heuer H, Sanders AF (eds) Perspectives in perception and action. Erlbaum, Hillsdale, NJ

    Google Scholar 

  • Kelso JAS, Scholz JP (1985) Cooperative phenomena in biological motion. In: Haken H (eds) Complex systems: operational approaches. Springer, Berlin, Heidelberg New York

    Google Scholar 

  • Kelso JAS, Schöner GS, Scholz JP, Haken H (1987) Phase-locked modes, phase transitions and component oscillators in biological motion. Phys Scr 35:79–87

    Google Scholar 

  • Kelao JAS, DelColle JD, Schöner GS (1990) Action-perception as a pattern formation process. In: Jeannerod M (eds) Attention and performance XIII. Erlbaum, Hillsdale, NJ, pp 136–169

    Google Scholar 

  • Schmidt RC, Turvey MT (1994) Phase-entrainment dynamics of visually coupled rhythmic movements. Biol Cybern 70:369–376

    Google Scholar 

  • Schmidt RC, Carello C, Turvey MT (1990) Phase transitions and critical fluctuations in the visual coordination of rhythmic movements between people. J Psychol Hum Percept Perform 16:227–247

    Google Scholar 

  • Schmidt RC, Beek P, Treffner PJ, Turvey MT (1991) Dynamical substructure of coordinated rhythmic movements. J Exp Psychol Hum Percept Perform 17:635–651

    Google Scholar 

  • Schmidt RC, Shaw BK, Turvey MT (1993) Coupling dynamics in interlimb coordination. J Exp Psychol Hum Percept Perform 19:397–415

    Google Scholar 

  • Scholz JP, Kelso JAS (1989) A quantitative approach to understanding the formation and change of coordinated movement patterns. J Mot Behav 21:122–144

    Google Scholar 

  • Swinnen S, Heuer H, Massion J, Casaer P (eds) (1994) The control and modulation of patterns of interlimb coordination: a multidisciplinary perspective. Academic Press, New York

    Google Scholar 

  • Turvey MT, Schmidt RC, Beek PJ (1993) Fluctuations in interlimb rhythmic coordination. In: Newell KM, Corcos DM (eds) Variability and motor control. Human Kinetics Publishers, Champaign, Ill

    Google Scholar 

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Affiliations

  1. Institut für Theoretische Physik und Synergetik, Universität Stuttgart, Pfaffenwaldring 57/4, D-70550, Stuttgart, Germany

    A. Fuchs, V. K. Jirsa & H. Haken

  2. Center for Complex Systems and Brain Sciences, Florida Atlantic University, 33431, Boca Raton, FL, USA

    A. Fuchs, H. Haken & J. A. Scott Kelso

Authors
  1. A. Fuchs
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  2. V. K. Jirsa
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  3. H. Haken
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  4. J. A. Scott Kelso
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Fuchs, A., Jirsa, V.K., Haken, H. et al. Extending the HKB model of coordinated movement to oscillators with different eigenfrequencies. Biol. Cybern. 74, 21–30 (1996). https://doi.org/10.1007/BF00199134

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  • DOI: https://doi.org/10.1007/BF00199134

Keywords

  • Time Series
  • Coordinate System
  • Phase Space
  • Relative Phase
  • Human Movement