Biological Cybernetics

, Volume 64, Issue 6, pp 485–495 | Cite as

Multifrequency behavioral patterns and the phase attractive circle map

  • G. C. deGuzman
  • J. A. S. Kelso
Article
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Abstract

With relative phase as a collective variable or order parameter, phase attractive dynamics can capture the temporally coherent behavior of a large number of different experimental systems. We present results from multifrequency coordination experiments in humans showing: a) that phase attraction persists especially for low order frequency ratios; b) that short-term jumps from one phase relation to another occur within a frequency ratio; c) that the most stable frequency-ratios are low order; and d) that transitions frequently occur from higher order (e.g. 5∶2, 4∶3) to lower order (2∶1, 1∶1) frequency ratios. We study a modified sine circle map with built-in phase attractive dynamics that qualitatively accounts for these results. In this phase-attractive map, patterns arise from competition between external driving and intrinsic phase attractive dynamics. The relative strength of extrinsic and intrinsic parameters determines the width of Arnol'd tongues, thereby influencing the delay or acceleration of irregular behavior. Behavioral complexity is inversely proportional to tongue width, thus accounting for the relative difficulty of performing different multifrequency behaviors and why “errors” in such behavior are often seen to occur.

Keywords

Sine Phase Relation Relative Strength Behavioral Pattern Phase Attraction 
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.
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References

  1. Aihara K, Namajiri T, Matsumoto G, Kotani M (1986) Phys Lett 116A:313Google Scholar
  2. Arnold VI (1965) Small denominators 1. Mappings of the circumference onto itself. Trans AMS Ser 2 46:213–284Google Scholar
  3. Bak P, Bohr T, Jensen MH (1984) Mode-locking and transition to chaos in dissipative systems. Phys Scr T 9:50–58Google Scholar
  4. Beek PJ (1989) Timing and phase locking in cascade juggling. Ecol Psych 2:55–96Google Scholar
  5. Bramble DM, Carrier DR (1983) Running and breathing in mammals. Science 219:251–256Google Scholar
  6. Cohen AH, Holmes PJ, Rand RH (1982) The nature of the coupling between segmental oscillators of the lamprey spinal generator for locomotion: a mathematical model. J Math Biol 13:345–369Google Scholar
  7. Deutsch D (1983) The generation of two isochronous sequences in parallel. Percept Psychophys 34:331–337Google Scholar
  8. Glazier JA, Libchaber A (1988) Quasi-periodicity and dynamical systems. IEEE Trans Circuits Systems 35:790–809Google Scholar
  9. Goldberger AL, Bhargava V, West BJ, Mandell AJ (1986) Some observations on the question: Is ventricular fibrillation “chaos”? Physica 19D:282–289Google Scholar
  10. Guevarra MR, Glass L, Shrier A (1981) Phase locking, period-doubling bifurcations, and irregular dynamics in periodically stimulated cardiac cells. Science 214:1350–1352Google Scholar
  11. Haken H (1983) Synergetics: an introduction. Nonequilibrium phase transitions and self-organization in physics, chemistry and biology, 3rd edn. Springer, Berlin Heidelberg New YorkGoogle Scholar
  12. Haken H (1987) Information compression in biological systems. Biol Cybern 56:11–17Google Scholar
  13. Haken H, Kelso JAS, Bunz H (1985) A theoretical model of phase transitions in human bimanual coordination. Biol Cybern 51:347–356Google Scholar
  14. Kay BA, Kelso JAS, Saltzman EL, Schöner G (1987) Space time behavior of single and bimanual rhythmic movements: Data and limit cycle model. J Exp Psychol: Human Percept Perf 13:178–192Google Scholar
  15. Kay BA, Saltzman EL, Kelso JAS (in press) Steady-state and perturbed rhythmical movements: dynamical models using a variety of analytical tools. J Exp Psychol: Human Percept PerfGoogle Scholar
  16. Kelso JAS (1981) On the oscillatory basis of movement. Bull Psychon Soc 18:63Google Scholar
  17. Kelso JAS (1984) Phase transitions and critical behavior in human bimanual coordination. Am J Physiol: Reg Integr Comp Physiol 15:R1000-R1004Google Scholar
  18. Kelso JAS, deGuzman GC (1989) Phase attractive dynamics and pattern selection in complex multifrequency behaviors. Soc Neurosci 15:174Google Scholar
  19. Kelso JAS, Holt KG (1980) Exploring a vibratory system analysis of human movement production. J Neurophys 43:1183–1196Google Scholar
  20. Kelso JAS, Scholz JP (1985) Cooperative phenomena in biological motion. In: Haken H (ed) Complex systems: operational approaches in neurobiology, physics and computers. Springer, Berlin Heidelberg New York, pp 124–149Google Scholar
  21. Kelso JAS, Schöner G (1987) Toward a physical (synergetic) theory of biological coordination. Springer Proceedings in Physics, 19. Springer, Berlin Heidelberg New York, pp 224–237Google Scholar
  22. Kelso JAS, Scholz JP, Schöner G (1986) Nonequilibrium phase transitions in coordinated biological motion: critical fluctuations. Phys Lett A 118:279–284Google Scholar
  23. Kelso JAS, Schöner G, Scholz JP, Haken H (1987) Phase-locked modes, phase transitions and component oscillators in biological motion. Phys Scr 35:79–87Google Scholar
  24. Kelso JAS, delColle, JD, Schöner G (1990) Action-perception as a pattern formation process. Attention and performance, XIII. Erlbaum, Hillsdale, NJ, pp 139–169Google Scholar
  25. Kuramato Y (1984) Chemical oscillations, waves, and turbulence. Springer, Berlin Heidelberg New YorkGoogle Scholar
  26. Mackay RS, Tresses C (1984) Transition to chaos for two-frequency systems. J Phys Lett 45:L741-L746Google Scholar
  27. Moulins M, Nagy F (1985) In: Selverston AI (ed) Model neural networks and behavior. Plenum Press, New York, p 49Google Scholar
  28. Povel DJ (1981) Internal representation of simple temporal patterns. J Exp Psychol: Hum Percept Perf 7:3–18Google Scholar
  29. Schmidt RC, Carello C, Turvey MT (1990) Phase transitions and critical fluctuations in the visual coordination of rhythmic movements between people. J Exp Psychol: Hum Percept Perf 16:227–247Google Scholar
  30. Schöner G, Kelso JAS (1988) A synergetic theory of environmentally-specified and learned patterns of human coordination. Biol Cyber 58:71–89Google Scholar
  31. Schöner G, Haken H, Kelso JAS (1986) A stochastic theory of phase transition in human hand movement. Biol Cybern 53:347Google Scholar
  32. Scholz JP, Kelso JAS (1989) A quantitative approach to understanding the formation and change of coordinated movement patterns. J Mot Behav 21:122–144Google Scholar
  33. Scholz JP, Kelso JAS, Schoner G (1987) Nonequilibrium phase transitions in coordinated biological motion: critical slowing and switching time. Phys Lett A 123:390–394Google Scholar
  34. Tuller B, Kelso JAS (1985) Coordination in normal and split-brain patients. Paper presented at Psychonomic Society, Boston, MassGoogle Scholar
  35. Tuller B, Kelso JAS (1989) Environmentally-specified patterns of movement coordination in normal and split-brain subjects. Exp Brain Res 75:306–316Google Scholar
  36. Von Holst E (1939/1973) Relative coordination as a phenomenon and as a method of analysis of central nervous function. Reprinted in: The collected papers of Erich von Holst: University of Miami Press, Coral Gables, FlaGoogle Scholar
  37. Yamanishi J, Kawato M, Suzuki R (1980) Two coupled oscillators as a model for the coordinated finger tapping by both hands. Biol Cybern 37:219–225Google Scholar

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • G. C. deGuzman
    • 1
  • J. A. S. Kelso
    • 1
  1. 1.Program in Complex Systems and Brain Sciences, Center for Complex SystemsFlorida Atlantic UniversityBoca RatonUSA

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