Journal of Biological Physics

, Volume 35, Issue 2, pp 127–147

Order Parameter Dynamics of Body-scaled Hysteresis and Mode Transitions in Grasping Behavior

  • T. D. Frank
  • M. J. Richardson
  • Stacy M. Lopresti-Goodman
  • M. T. Turvey
Original Paper


Several experimental studies have shown that human grasping behavior exhibits a transition from one-handed to two-handed grasping when to-be-grasped objects become larger and larger. The transition point depends on the relative size of objects measured in terms of human body-scales. Most strikingly, the transitions between the two different behavioral ‘modes’ of grasping exhibit hysteresis. That is, one-to-two hand transitions and two-to-one hand transitions occur at different relative object sizes when objects are scaled up or down in size. In our study we approach body-scaled hysteresis and mode transitions in grasping by exploiting the notion that human behavior in general results from self-organization and satisfies appropriately-defined order parameter equations. To this end, grasping transitions and grasping hysteresis are discussed from a theoretical perspective in analogy to cognitive processes defined by Haken’s neural network model for pattern recognition. In doing so, issues such as the exclusivity of grasping modes, biomechanical constraints, mode-mode interactions, single subject behavior and population behavior are explored.


Order parameters Hysteresis Grasping 


  1. 1.
    Cesari, P., Newell, K.M.: Body-scaled transitions in human grip configurations. J. Exp. Psychol. Hum. Percept. Perform. 26, 1657–1668 (1999)Google Scholar
  2. 2.
    Cesari, P., Newell, K.M.: Scaling of human grip configurations. J. Exp. Psychol. Hum. Percept. Perform. 25, 927–935 (1999)CrossRefGoogle Scholar
  3. 3.
    Newell, K.M., Scully, D.M., McDonald, P.V., Baillargeon, R.: Task constraints and infant grip configuration. Dev. Psychobiol. 22, 817–832 (1989)CrossRefGoogle Scholar
  4. 4.
    Newell, K.M., Scully, D.M., Tenenbaum, F., Hardiman, S.: Body scale and the development of prehension. Dev. Psychobiol. 22, 1–13 (1989)CrossRefGoogle Scholar
  5. 5.
    van der Kamp, J., Savelsbergh, G.J.P., Davis, W.E.: Body-scaled ratio as a control parameter for prehension in 5- to 9-year old children. Dev. Psychobiol. 33, 351–361 (1998)CrossRefGoogle Scholar
  6. 6.
    van Hof, P., van der Kamp, J., Savelsbergh, G.J.P.: The relation of unimanual and bimanual reaching to crossing the midline. Child Dev. 73, 1353–1362 (2002)CrossRefGoogle Scholar
  7. 7.
    Richardson, M.J., Marsh, K.L., Baron, R.M.: Judging and actualizing intrapersonal and interpresonal affordances. J. Exp. Psychol. Hum. Percept. Perform. 33, 845–859 (2007)CrossRefGoogle Scholar
  8. 8.
    Marsh, K.L., Richardson, M.J., Baron, R.M.: Contrasting approaches to perceiving and acting with others. Ecol. Psychol. 18, 1–38 (2006)CrossRefGoogle Scholar
  9. 9.
    Gibson, J.J.: The Ecological Approach to Visual Perception. Houghton-Mifflin, Boston (1979)Google Scholar
  10. 10.
    Michaels, C.F., Carello, C.: Direct Perception. Prentice-Hall, Inc., Englewood Cliffs, N.J. (1981)Google Scholar
  11. 11.
    Turvey, M.T.: Affordances and prospective control: an outline of the ontology. Ecol. Psychol. 4(3), 173–187 (1992)CrossRefGoogle Scholar
  12. 12.
    Warren, W.H.: Perceiving affordances: visual guidance of stair climbing. J. Exp. Psychol. Hum. Percept. Perform. 10, 683–703 (1984)CrossRefGoogle Scholar
  13. 13.
    Beek, P.J., Peper, C.E., Stegeman, D.F.: Dynamical models of movement coordination. Hum. Mov. Sci. 14, 573–608 (1995)CrossRefGoogle Scholar
  14. 14.
    Frank, T.D.: On a nonlinear master equation and the Haken-Kelso-Bunz model. J. Biol. Phys. 30, 139–159 (2004)CrossRefGoogle Scholar
  15. 15.
    Frank, T.D.: Nonlinear Fokker-Planck Equations: Fundamentals and Applications. Springer, Berlin (2005)MATHGoogle Scholar
  16. 16.
    Frank, T.D., Daffertshofer, A., Beek, P.J., Haken, H.: Impacts of noise on a field theoretical model of the human brain. Physica D 127, 233–249 (1999)MATHCrossRefADSGoogle Scholar
  17. 17.
    Frank, T.D., Daffertshofer, A., Peper, C.E., Beek, P.J., Haken, H.: Towards a comprehensive theory of brain activity: coupled oscillator systems under external forces. Physica D 144, 62–86 (2000)MATHCrossRefADSMathSciNetGoogle Scholar
  18. 18.
    Frank, T.D., Michelbrink, M., Beckmann, H., Schöllhorn, W.I.: On a quantitative dynamical systems approach to differential learning: self-organization principle and order parameter equations. Biol. Cybern. 98, 19–31 (2008)MATHCrossRefGoogle Scholar
  19. 19.
    Haken, H.: Principles of Brain Functioning. Springer, Berlin (1996)MATHGoogle Scholar
  20. 20.
    Jirsa, V.K., Kelso, J.A.S.: Coordination Dynamics: Issues and Trends. Springer, Berlin (2004)Google Scholar
  21. 21.
    Kelso, J.A.S.: Phase transitions and critical behavior in human bimanual coordination. Am. J. Physiol. 15, R1000–R1004 (1984)Google Scholar
  22. 22.
    Kelso, J.A.S.: Dynamic Patterns - The Self-organization of Brain and Behavior. MIT Press, Cambridge (1995)Google Scholar
  23. 23.
    Mechsner, F., Kerzel, D., Knoblich, G., Prinz, W.: Perceptual basis of bimanual coordination. Nature 414, 69–73 (2001)CrossRefADSGoogle Scholar
  24. 24.
    Peper, C.E., Beek, P.J., van Wieringen, P.C.W.: Frequency-induced transitions in bimanual tapping. Biol. Cybern. 73, 301–309 (1995)CrossRefGoogle Scholar
  25. 25.
    Schöner, G.S., Kelso, J.A.S.: A synergetic theory of environmentally-specified and learned patterns of movement coordination. I. Relative phase dynamics. Biol. Cybern. 58, 71–80 (1988)CrossRefGoogle Scholar
  26. 26.
    Schöner, G.S., Kelso, J.A.S.: A synergetic theory of environmentally-specified and learned patterns of movement coordination. II. Component oscillator dynamics. Biol. Cybern. 58, 81–89 (1988)CrossRefGoogle Scholar
  27. 27.
    Sternad, D., Turvey, M.T., Saltzman, E.L.: Dynamics of 1:2 coordination: generalizing relative phase to n:m rhythms, sources of symmetry breaking, temporal scaling, latent 1:1, and bistability. J. Mot. Behav. 31, 207–247 (1999)CrossRefGoogle Scholar
  28. 28.
    Tass, P., Wunderlin, A., Schanz, M.: A theoretical model of sinusoidal forearm tracking with delayed visual feedback. J. Biol. Phys. 21, 83–112 (1995)CrossRefGoogle Scholar
  29. 29.
    Turvey, M.T.: Coordination. Am. Psychol. 45, 938–953 (1990)CrossRefGoogle Scholar
  30. 30.
    Haken, H.: Synergetics: Introduction and Advanced Topics. Springer, Berlin (2004)Google Scholar
  31. 31.
    Lee, D.N., Reddish, D.E.: Plummeting gannets: a paradigm of ecological optics. Nature 293, 293–294 (1981)CrossRefADSGoogle Scholar
  32. 32.
    Turvey, M.T.: Dynamic touch. Am. Psychol. 51, 1134–1152 (1996)CrossRefGoogle Scholar
  33. 33.
    Withagen, R.: The pick-up of non-specifying variables does not entail indirect perception. Ecol. Psychol. 16, 237–253 (2004)CrossRefGoogle Scholar
  34. 34.
    Lee, D.N., Young, D.S., Reddish, D.E., Lough, S., Clyton, T.M.H.: Visual timing in hitting an accelerating ball. Q. J. Exp. Psychol. 35, 333–346 (1983)Google Scholar
  35. 35.
    Savelsbergh, G.J.P., Whiting, H.T.A., Bootsma, R.J.: Grasping tau. J. Exp. Psychol. Hum. Percept. Perform. 17, 315–322 (1991)CrossRefGoogle Scholar
  36. 36.
    Fitzpatrick, P., Carello, C., Schmidt, R.C., Corey, D.: Haptic and visual perception of an affordance for upright posture. Ecol. Psychol. 6(4), 265–287 (1994)CrossRefGoogle Scholar
  37. 37.
    Haken, H.: Synergetic Computers and Cognition. Springer, Berlin (1991)MATHGoogle Scholar
  38. 38.
    Fuchs, A., Haken, H.: Pattern recognition and associative memory as dynamical processes in a synergetic system. I. Translational invariance, selective attention and decomposition of scene. Biol. Cybern. 60, 17–22 (1988)MATHMathSciNetGoogle Scholar
  39. 39.
    Fuchs, A., Haken, H.: Pattern recognition and associative memory as dynamical processes in a synergetic system. II. Decomposition of complex scenes, simultaneous invariance with respect to translation, rotation, and scaling. Biol. Cybern. 60, 107–109 (1988)CrossRefMathSciNetGoogle Scholar
  40. 40.
    Haken, H.: Nonequilibrium phase transitions in pattern recognition and associative memory. Z. Phys. B 70, 121–123 (1988)CrossRefADSMathSciNetGoogle Scholar
  41. 41.
    Ditzinger, T., Haken, H.: Oscillations in the perception of ambigious patterns: a model based on synergetics. Biol. Cybern. 61, 279–287 (1989)CrossRefMathSciNetGoogle Scholar
  42. 42.
    Bressloff, P.C.: Neural networks, lattice instantons, and the anti-integrable limit. Phys. Rev. Lett. 75, 962–965 (1995)CrossRefADSGoogle Scholar
  43. 43.
    Bressloff, P.C.: A self-organizing neural network in the weak-coupling limit. Physica D 110, 195–208 (1997)MATHCrossRefADSMathSciNetGoogle Scholar
  44. 44.
    Bressloff, P.C., Roper, P.: Stochastic dynamics of the diffusive Haken model with subthreshold periodic forcing. Phys. Rev. E 58, 2282–2287 (1998)CrossRefADSGoogle Scholar
  45. 45.
    Turvey, M.T.: Impredicativity, dynamics, and the perception-action divide. In: Jirsa, V.K., Kelso, J.A.S. (eds.) Coordination Dynamics: Issues and Trends, vol. I, pp. 1–20. Springer, New York (2004)Google Scholar
  46. 46.
    Warren, W.H.: The dynamics of perception and action. Psychol. Rev. 113, 358–389 (2006)CrossRefGoogle Scholar

Copyright information

© Springer Science + Business Media B.V. 2009

Authors and Affiliations

  • T. D. Frank
    • 1
  • M. J. Richardson
    • 2
  • Stacy M. Lopresti-Goodman
    • 1
  • M. T. Turvey
    • 1
    • 3
  1. 1.Center for the Ecological Study of Perception and Action, Department of Psychology, 406 Babbidge Road, Unit 1020University of ConnecticutStorrsUSA
  2. 2.Department of PsychologyColby CollegeWatervilleUSA
  3. 3.Haskins LaboratoriesNew HavenUSA

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