Biological Cybernetics

, Volume 51, Issue 5, pp 347–356 | Cite as

A theoretical model of phase transitions in human hand movements

  • H. Haken
  • J. A. S. Kelso
  • H. Bunz


Earlier experimental studies by one of us (Kelso, 1981a, 1984) have shown that abrupt phase transitions occur in human hand movements under the influence of scalar changes in cycling frequency. Beyond a critical frequency the originally prepared out-of-phase, antisymmetric mode is replaced by a symmetrical, in-phase mode involving simultaneous activation of homologous muscle groups. Qualitavely, these phase transitions are analogous to gait shifts in animal locomotion as well as phenomena common to other physical and biological systems in which new “modes” or spatiotemporal patterns arise when the system is parametrically scaled beyond its equilibrium state (Haken, 1983). In this paper a theoretical model, using concepts central to the interdisciplinary field of synergetics and nonlinear oscillator theory, is developed, which reproduces (among other features) the dramatic change in coordinative pattern observed between the hands.


Phase Transition Muscle Group Nonlinear Oscillator Critical Frequency Spatiotemporal Pattern 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Baldissera, F., Cavallari, P., Civaschi, P.: Preferential coupling between voluntary movements of ipsilateral limbs. Neurosci. Let. 34, 95–100 (1982)Google Scholar
  2. Cohen, L.: Synchronous bimanual movements performed by homologous and non-homologous muscles. Percept. Mot. Skills 32, 639–644 (1971)Google Scholar
  3. Cohen, A.H., Holmes, P.J., Rand, R.H.: The nature of the coupling between segmental oscillators of the lamprey spinal generator for locomotion: a mathematical model. J. Math. Biol. 13, 345–369 (1982)Google Scholar
  4. Goodman, D., Kelso, J.A.S.: Exploring the functional significance of physiological tremor: a biospectroscopic approach. Exp. Brain Res. 49, 419–431 (1983)Google Scholar
  5. Grillner, S.: Possible analogies in the control of innate motor acts and the production of sound in speech. In: Speech motor control. Grillner, S., Lindblom, B., Lubker, J., Persson, A., eds. Oxford: Pergamon Press 1982Google Scholar
  6. Haken, H.: Cooperative phenomena in system far from thermal equilibrium and in nonphysical systems. Rev. Mod. Phys. 47, 67–121 (1975)Google Scholar
  7. Haken, H.: Synergetics: An introduction. 3rd. ed. Berlin, Heidelberg, New York: Springer 1983Google Scholar
  8. Haken, H.: Laser light dynamics. Amsterdam: North-Holland 1984Google Scholar
  9. Kelso, J.A.S.: On the oscillatory basis of movement. Bull. Psychon. Soc. 18, 63 (1981a)Google Scholar
  10. Kelso, J.A.S.: Contrasting perspectives on order and regulation in movement. In: Attention and performance. IX. Long, J., Baddeley, A., eds. Hillsdale, New York: Erlbaum 1981bGoogle Scholar
  11. Kelso, J.A.S.: Invited paper presented at Kroc foundation conference on nonlinear mechanisms in brain function (Santa Barbara, CA, March 1–5 1982)Google Scholar
  12. Kelso, J.A.S.: Phase transitions and critical behavior in human bimanual coordination. Am. J. Physiol.: Reg. Integ. Comp. 15, R1000-R1004 (1984)Google Scholar
  13. Kelso, J.A.S., Holt, K.G., Rubin, P., Kugler, P.N.: Patterns of human interlimb coordination emerge from nonlinear limit cycle oscillatory processes: theory and data. J. Mot. Behav. 13, 226–261 (1981)Google Scholar
  14. Kelso, J.A.S., Southard, D.L., Goodman, D.: On the nature of human interlimb coordination. Science 203, 1029–1031 (1979)Google Scholar
  15. Landau, L.: The theory of phase transitions. Nature 138, 840 (1936). Also In: Collected papers of L.D. Landau. Ter Har, D., ed. Oxford: Pergamon Press 1965Google Scholar
  16. MacKenzie, C.L., Patla, A.E.: Breakdown in rapid bimanual finger tapping as a function of orientation and plasing. Soc. Neurosci. (Abstract) (1983)Google Scholar
  17. Schmidt, R.A.: Motor control and learning: a behavioral emphasis. Champaign, IL: Human Kinetics 1982Google Scholar
  18. Shapiro, D.C.: Personal communication to J.A.S. Kelso (1981)Google Scholar
  19. Shik, M.L., Severin, F.V., Orlovskii, G.N.: Control of walking and running by means of electrical stimulation of the mid-brain. Biofizyka 11, 659–666 (1966)Google Scholar
  20. Tuller, B., Kelso, J.A.S.: The kinematics of bimanual movements in commissurotomy patients. Paper presented at the International Neuropsychology Society Meeting (Houston, TX, February 1984)Google Scholar
  21. Tuller, B., Kelso, J.A.S., Harris, K.S.: Interarticulator phasing as an index of temporal regularity in speech. J. Exp. Psychol.: Hum. Percept. Perform. 8, 460–472 (1982)Google Scholar
  22. Willis, J.B.: On the interaction between spinal locomotor generators in quadrupeds. Brain Res. 2, 171–204 (1980)Google Scholar
  23. Wilson, K.G.: Problems in physics with many scales of length. Sci. Am. 241, 158–179 (1979)Google Scholar
  24. Yamanishi, J., Kawato, M., Suzuki, R.: Two coupled oscillators as a model for the coordinated finger tapping by both hands. Biol. Cybern. 37, 219–225 (1980)Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • H. Haken
    • 1
  • J. A. S. Kelso
    • 2
    • 3
  • H. Bunz
    • 1
  1. 1.1. Institut für Theoretische PhysikUniversität StuttgartStuttgart 80Germany
  2. 2.Haskins LaboratoriesNew HavenUSA
  3. 3.Department of Psychology and Biobehavioral SciencesUniversity of ConnecticutStorrsUSA

Personalised recommendations