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. FrankEmail author
  • M. Michelbrink
  • H. Beckmann
  • W. I. Schöllhorn
Original Paper


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.


Learning Rate Dynamical System Approach Motor Control System Differential Learning Dynamical System Perspective 
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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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • T. D. Frank
    • 1
    • 2
    Email author
  • 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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