Biological Cybernetics

, Volume 98, Issue 1, pp 19–31 | Cite as

A quantitative dynamical systems approach to differential learning: self-organization principle and order parameter equations

  • T. D. Frank
  • M. Michelbrink
  • H. Beckmann
  • W. I. Schöllhorn
Original Paper

Abstract

Differential learning is a learning concept that assists subjects to find individual optimal performance patterns for given complex motor skills. To this end, training is provided in terms of noisy training sessions that feature a large variety of between-exercises differences. In several previous experimental studies it has been shown that performance improvement due to differential learning is higher than due to traditional learning and performance improvement due to differential learning occurs even during post-training periods. In this study we develop a quantitative dynamical systems approach to differential learning. Accordingly, differential learning is regarded as a self-organized process that results in the emergence of subject- and context-dependent attractors. These attractors emerge due to noise-induced bifurcations involving order parameters in terms of learning rates. In contrast, traditional learning is regarded as an externally driven process that results in the emergence of environmentally specified attractors. Performance improvement during post-training periods is explained as an hysteresis effect. An order parameter equation for differential learning involving a fourth-order polynomial potential is discussed explicitly. New predictions concerning the relationship between traditional and differential learning are derived.

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References

  1. Adams JA (1971) A closed-loop theory of motor learning. J Motor Behav 3: 111–149Google Scholar
  2. Amazeen PG, Amazeen E, Turvey MT (1998) Dynamics of human intersegmental coordination: theory and research. In: Rosenbaum DA, Collyer CE(eds) Timing of behavior. MIT, Cambridge, pp 237–259Google Scholar
  3. Beckmann H (2003) MA Thesis: Vergleich von Techniktrainingsansätzen im Kugelstoßen (in German). University of Münster, MünsterGoogle Scholar
  4. Beckmann H, Schöllhorn W (2003) Differential learning in shot put. In: Schöllhorn WI, Bohn C, Jäger JM, Schaper H, Alichmann M(eds) European workshop on movement sciences. Sport & Buch Strauß, Cologne, pp 68–68Google Scholar
  5. Beek PJ, Peper CE, Stegeman DF (1995) Dynamical models of movement coordination. Hum Movement Sci 14: 573–608CrossRefGoogle Scholar
  6. Beek PJ, Turvey MT (1992) Temporal patterning in cascade juggling. J Exp Psychol - Hum Percept Perform 18: 934–947PubMedCrossRefGoogle Scholar
  7. Bernstein NA (1967) The coordination and regulation of movements. Pergamon, OxfordGoogle Scholar
  8. Daffertshofer A, van den Berg C, Beek PJ (1999) A dynamical model for mirror movements. Physica D 132: 243–266CrossRefGoogle Scholar
  9. Frank TD (2005a) Nonlinear Fokker–Planck equations: fundamentals and applications. Springer, BerlinGoogle Scholar
  10. Frank TD (2005b) On the M. Phys Rev E 72: 041703CrossRefGoogle Scholar
  11. Haken H (1975) Cooperative phenomena in systems far from thermal equilibrium and in nonphysical systems. Rev Mod Phys 47: 67–121CrossRefGoogle Scholar
  12. Haken H (1996) Principles of brain functioning. Springer, BerlinGoogle Scholar
  13. Haken H (2004) Synergetics: introduction and advanced topics. Springer, BerlinGoogle Scholar
  14. Henry RM, Rogers DE (1960) Increased response latency for complicated movements and a “memory drum” theory of neuromotor reactions. Res Quat 31: 448–457Google Scholar
  15. Horsthemke W, Lefever R (1984) Noise-induced transitions. Springer, BerlinGoogle Scholar
  16. Humpert V (2004) MA thesis: Vergleichende Analyse von Techniktrainingansätzen zum Tennisaufschlag (in German). University of Münster, MünsterGoogle Scholar
  17. Humpert V, Schöllhorn WI (2006) Vergleich von T. In: Ferrouti A, Remmert H(eds) Trainingswissenschaften im F. Czwalina, Hamburg, pp 121–124Google Scholar
  18. Huys R, Daffertshofer A, Beek PJ (2004) Multiple time scales and subsystem embedding in the learning of juggling. Hum Mov Sci 23: 315–336PubMedCrossRefGoogle Scholar
  19. Jirsa VK, Kelso JAS (2004) Coordination dynamics: issues and trends. Springer, BerlinGoogle Scholar
  20. Kay BA (1988) The dimensionality of movement trajectories and the degrees of freedom problem. Hum Mov Sci 7: 343–364CrossRefGoogle Scholar
  21. Keele SW (1968) Movement control in skilled performance. Psychol Bull 70: 387–403CrossRefGoogle Scholar
  22. Kelso JAS (1995) Dynamic patterns—the self-organization of brain and behavior. MIT, CambridgeGoogle Scholar
  23. Neda Z, Ravasz E, Vicsek T, Brechet Y, Barabasi AL (2000) Physics of the rhythmic applause. Phys Rev E 61: 6987–6992CrossRefGoogle Scholar
  24. Patanarapeelert K, Frank TD, Beek PJ, Friedrich R, Tang IM (2006) Theoretical analysis of destabilization resonances in time-delayed stochastic second order dynamical systems and some implications for human motor control. Phys Rev E 73: 021901CrossRefGoogle Scholar
  25. Peper CE, Beek PJ (1998) Distinguishing between the effects of frequency and amplitude on interlimb coupling in tapping a 2:3 polyrhythm. Exp Brain Res 118: 78–92PubMedCrossRefGoogle Scholar
  26. Peper CE, Beek PJ, van Wieringen PCW (1995) Multifrequency coordination in bimanual tapping: a symmetrical coupling and signs of supercriticality. J Exp Psychol - Hum Percept Perform 21: 1117–1138CrossRefGoogle Scholar
  27. Plischke M, Bergersen B (1994) Equilibrium statistical physics. World Scientific, SingaporGoogle Scholar
  28. Römer J, Schöllhorn WI, Jaitner T (2003) Differentielles lernen bei der Aufschlagannahme im Volleyball. In: Krug J, Müller T (eds) Messplätze, Messtraining, Motorisches Lernen (in German). Academia Verlag, Sankt Augustin, pp 129–133Google Scholar
  29. Schmidt RA, Lee TD (1999) Motor control and learning: a behavioral emphasis. Human Kinetics, ChampaignGoogle Scholar
  30. Schöllhorn WI (1999a) Individualität - ein vernachlässigter Parameter? (in German) Leistungssport 2:4–11Google Scholar
  31. Schöllhorn WI (1999b) Practical consequences of biomechanically determined individuality and fluctuations on motor learning. In: Herzog W, Jinha A (eds) International Society of Biomechanics XVIIth Congress. Calgary, p 147Google Scholar
  32. Schöllhorn WI (2000) Applications of systems dynamic principles to technique and strength training. Acta Acad Estonia 8: 25–37Google Scholar
  33. Schöllhorn WI, Beckmann H, Michelbrink M, Trockel M, Sechelmann M, Davids K (2006) Does noise provide a basis for unifying different motor learning theories?. Int J Sport Psychol 2: 34–42Google Scholar
  34. Schöllhorn WI, Sechelmann M, Trockel M, Westers R (2004) Nie das Richtige trainieren, um richtig zu spielen (in German). Leistungsport 5:13–17Google Scholar
  35. Scholz JP, Kelso JAS, Schöner GS (1987) Non-equilibrium phase transitions in coordinated biological motion: critical slowing down and switching time. Phys Lett A 123: 390–394CrossRefGoogle Scholar
  36. Schöner GS (1989) Learning and recall in a dynamic theory of coordination patterns. Biol Cybern 62: 39–54PubMedCrossRefGoogle Scholar
  37. Schöner GS, Haken H, Kelso JAS (1986) A stochastic theory of phase transitions in human hand movement. Biol Cybern 53: 247–257PubMedCrossRefGoogle Scholar
  38. Schöner GS, Kelso JAS (1988a) A synergetic theory of environmentally-specified and learned patterns of movement coordination. I. R. Biol Cybern 58: 71–80PubMedCrossRefGoogle Scholar
  39. Schöner GS, Kelso JAS (1988b) A synergetic theory of environmentally-specified and learned patterns of movement coordination. II. Component oscillator dynamics. Biol Cybern 58: 81–89PubMedCrossRefGoogle Scholar
  40. Schöner GS, Zanone PG, Kelso JAS (1992) Learning as change in coordination dynamics. J Motor Behav 64: 455–462Google Scholar
  41. Shea CH, Shebilske WL, Worchel S (1993) Motor learning and control. Prentice Hall, Englewood CliffsGoogle Scholar
  42. Shea CH, Wulf G (2005) Schema theory: a critical appraisal and reevaluation. J Motor Behav 37: 85–101CrossRefGoogle Scholar
  43. Sternad D (2000) Debates in dynamics: a dynamical systems perspective on action and perception. Hum Mov Sci 19: 407–423CrossRefGoogle Scholar
  44. Sternad D, Duarte M, Katsumata H, Schaal S (2001) Dynamics of a bouncing ball in human performance. Phys Rev E 63: 011902CrossRefGoogle Scholar
  45. Turvey MT (1990) Coordination. Am Psychol 45: 938–953PubMedCrossRefGoogle Scholar
  46. van Rossum JHA (1990) Schmidt’s schema theory: the empirical base of the variability of practice hypothesis. Hum Mov Sci 9: 387–435CrossRefGoogle Scholar
  47. Wallenstein GV, Kelso JAS, Bressler SL (1995) Phase transitions in spatiotemporal patterns of brain activity and behavior. Physica D 84: 626–634CrossRefGoogle Scholar
  48. Welminski D (2005) MA thesis: Vergleich von Techniktrainingsansätzen im leichtathletischen Hochsprung (in German). University of Münster, MünsterGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • T. D. Frank
    • 1
    • 2
  • M. Michelbrink
    • 3
  • H. Beckmann
    • 4
  • W. I. Schöllhorn
    • 3
  1. 1.Institute for Theoretical PhysicsUniversity of MünsterMünsterGermany
  2. 2.Center for the Ecological Study of Perception and ActionUniversity of ConnecticutStorrsUSA
  3. 3.Institute for Sport ScienceUniversity of MainzMainzGermany
  4. 4.Institute of Sport ScienceUniversity of MünsterMünsterGermany

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