Modeling Rhythmic Interlimb Coordination: Beyond the Haken–Kelso–Bunz Model

  title={Modeling Rhythmic Interlimb Coordination: Beyond the Haken–Kelso–Bunz Model},
  author={Peter Jan Beek and C. E. Peper and Andreas Daffertshofer},
  journal={Brain and Cognition},
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… 

Dynamical Models of Rhythmic Interlimb Coordination

The empirically observed stability characteristics of rhythmic interlimb coordination have been modeled in terms of gradient dynamics of the (order) parameter that defines the coordination modes, but the high level of abstraction of these models precludes gaining insight into how the stability features result from underlying processes and system properties.

Dynamics of multifrequency coordination using parametric driving: theory and experiment

The description of unimanual coordination leads to a mechanism for phase transitions that is distinct from that seen in the HKB model, and the existence of two types of transitions in the extended theory, phase-mediated and amplitude-mediated transitions.

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A step-wise approach to a model that predicts the dynamics of inter-human movement coordination and can directly be implemented to enrich human–robot interaction.

A Computational Model for Rhythmic and Discrete Movements in Uni- and Bimanual Coordination

It is shown that a physiologically motivated model of a CPG can not only generate simple rhythmic movements with only a small set of parameters, but can also produce discrete movements if the CPG is fed with an exponentially decaying phasic input.

Effector dynamics of rhythmic wrist activity and its implications for (modeling) bimanual coordination.

Stabilization of bimanual coordination due to active interhemispheric inhibition: a dynamical account

A dynamical model is derived to account for the patterns of brain activity observed during stable performance of bimanual multifrequency patterns, as well as during behavioral instabilities in the form of phase transitions between such patterns.

The Dynamical Organization of Limb Movements

  • R. Huys
  • Psychology
    Nonlinear Dynamics in Human Behavior
  • 2011
The early 1980s saw the development of a new perspective on motor control inspired by theories of self-organization and dynamical systems theory, which resulted in a detailed documentation of the relation between oscillator properties and task requirements.

The Excitator as a Minimal Model for the Coordination Dynamics of Discrete and Rhythmic Movement Generation

The authors show analytically and numerically that the sigmoidal coupling leads to convergence phenomena in phase space, whereas the Haken-Kelso-Bunz coupling displays convergent as well as divergent behaviors.

The stability of rhythmic movement coordination depends on relative speed: the Bingham model supported

The central finding was that the stability of rhythmic movement coordination does depend on relative speed and, thus, all three of the hypotheses contained in the original Bingham model are supported.



Patterns of human interlimb coordination emerge from the properties of non-linear, limit cycle oscillatory processes.

An initial attempt to offer a principled solution to a fundamental problem of movement identified by Bernstein (1967), namely, how the degrees of freedom of the motor system are regulated, and the tentative claim that coordination and control are emergent consequences of dynamical interactions among non-linear, limit cycle oscillatory processes.

Space-time behavior of single and bimanual rhythmical movements: data and limit cycle model.

The abstract, dynamical model offers a unified treatment of a number of fundamental aspects of movement coordination and control in terms of low-dimensional (nonlinear) dissipative dynamics, with linear stiffness as the only control parameter.

Distinguishing between the effects of frequency and amplitude on interlimb coupling in tapping a 2:3 polyrhythm

The results support the time-delay version of the model, in which differential (loss of) stability of coordination modes results from differential dependence on movement amplitude, but overall coupling strength is related reciprocally to movement frequency squared.

Are frequency-induced transitions in rhythmic coordination mediated by a drop in amplitude?

It is suggested that frequency-induced transitions in coordinated rhythmic movements may not be mediated by a drop in amplitude and that alternative directions in modeling may have to be considered.

A comparison of intra- and interpersonal interlimb coordination: coordination breakdowns and coupling strength.

Intra- and interpersonal interlimb coordination of pendulums swung from the wrist was investigated and the properties observed were those predicted by a dynamical model of rhythmic coordination that considers the coordinated limbs coupled to be nonlinear oscillators.