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HKB model

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The Haken-Kelso-Bunz model (or HKB model) is a mathematical formulation that quantitatively describes and predicts how elementary forms of coordinated behavior arise and change adaptively as a result of nonlinear interactions among components.

Kelso and his colleagues demonstrated that many of the complexities of coordinated motor behavior in complex, multi-degree-of-freedom systems can be derived from relatively simple, but nonlinear mathematical laws. For a review of this work see Kelso et al. (1987) and Schöner and Kelso (1988)[1] In particular, Kelso developed a mathematical model in collaboration with the eminent theoretical physicist Hermann Haken, the father of laser theory and synergetics. This "HKB model" was able to derive basic forms of coordination observed in Kelso's experiments using a system of nonlinear relations between individual coordinating elements[2] The HKB model explained and predicted experimental observations such as "critical slowing down", and "enhanced fluctuations" associated with instability and dramatic changes in coordination. Later extensions of HKB accommodated the effects of noise, broken symmetry, multiple interacting heterogeneous components, recruitment-annihilation processes, parametric stabilization, and the role of changing environments on coordination[3]


  1. G. Schöner and J.A. Kelso (1988), "Dynamic pattern generation in behavioral and neural systems." Science vol. 239, p. 1513-1520; J.A.S. Kelso, et al. (1987), " Phase-locked modes, phase transitions and component oscillators in coordinated biological motion." Physica Scripta vol. 35, p. 79-87.
  2. Haken, H., Kelso, J.A.S., & Bunz, H. (1985). A theoretical model of phase transitions in human hand movements. Biological Cybernetics, 51, 347-356.
  3. For recent review see Kelso, J.A.S. (2009). Coordination Dynamics. In R.A. Meyers (Ed.) Encyclopedia of Complexity and System Science, Springer: Heidelberg.
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