Modeling rhythmic interlimb coordination: beyond the Haken-Kelso-Bunz model.

Although the Haken-Kelso-Bunz (HKB) model was originally formulated to account for phase transitions in bimanual movements, it evolved, through experimentation and conceptual elaboration, into a fundamental formal construct for the experimental study of rhythmically coordinated movements in general. The model consists of two levels of formalization: a potential defining the stability properties of relative phase and a system of coupled limit cycle oscillators defining the individual limb movements and their interactions. Whereas the empirical validity of the potential is well established, the validity of the formalization in terms of coupled oscillators is questionable, both with regard to the assumption that individual limb movements are limit cycle oscillators with (only) two active degrees of freedom and with regard to the postulated coupling. To remedy these limitations a more elaborate system of coupled oscillators is outlined, comprising two coupled limit cycle oscillators at the neural level, each of which is coupled to a linearly damped oscillator, representing the end-effectors. Copyright 2001 Elsevier Science (USA).