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Abstract. Schoner [Schoner G (1995) Ecol Psychol 7: 291 314] argued that the relative phase dynamics of rhythmic interlimb coordination may be attributed to the timing level in that the stability properties of the relative phase are largely independent of dynamical principles operating at the goal level, such as those related to the maintenance of a particular amplitude or target position. Yet, according to the coupling functions in the coupled oscillator model proposed by Haken et al. [Haken H, Kelso JAS, Bunz H (1985) Biol Cybern 51:347 356], the effect of frequency on the stability properties of relative phase is either wholly or partially mediated by frequency-induced changes in amplitude, implying that the relative phase dynamics strongly depends on spatial factors. In order to distinguish between these contrasting interpretations of the organizational principles underwriting the phase dynamics of interlimb coordination, an experiment was conducted in which the effects of frequency and amplitude on the stability of relative phase were separated. Six subjects performed both in-phase and antiphase coordination patterns at seven different frequencies and three different amplitudes. Two measures of pattern stability were used, the standard deviation of relative phase and the exponent of the relaxation process following phasic perturbations of relative phase. According to both measures, pattern stability decreased with increasing frequency, whereas the amplitude manipulation only had a significant effect on the standard deviation of relative phase. This result was interpreted to imply that the organizational principles at the... [ABSTRACT FROM AUTHOR]

Abstract. Various stability features of bimanual rhythmic coordination, including phase transitions, have been modeled successfully by means of a one-dimensional equation of motion for relative phase obeying a gradient dynamics, the Haken-Kelso-Bunz model. The present study aimed at assessing pattern stability for stationary performance and estimating the model parameters (a, b, and Q) for the stochastic extension of this model. Estimates of a and b allowed for reconstruction of the potential defining the gradient dynamics. Two coordination patterns between the forearms (in-phase, antiphase) were performed at seven different frequencies. Model parameters were estimated on the basis of an exponential decay parameter describing the relaxation behavior of continuous relative phase following a mechanical perturbation. Variability of relative phase and relaxation time provided measures of pattern stability. Although the predicted inverse relation between pattern stability and movement frequency was observed for the lower tempo conditions, it was absent for the higher tempos, reflecting the influence of task constraints. No statistically significant differences in stability were observed between the two coordination modes, indicating the influence of intention. The reconstructed potential reflected the observed stability features, underscoring the adequacy of the parameter estimations. The relaxation process could not be captured adequately by means of a simple exponential decay function but required an additional oscillatory term. In accordance with previous assumptions... [ABSTRACT FROM AUTHOR]

This article presents a brief retrospective on the Haken–Kelso–Bunz (HKB) model of certain dynamical properties of human movement. Though unanticipated, HKB introduced, and demonstrated the power of, a new vocabulary for understanding behavior, cognition and the brain, revealed through a visually compelling mathematical picture that accommodated highly reproducible experimental facts and predicted new ones. HKB stands as a harbinger of paradigm change in several scientific fields, the effects of which are still being felt. In particular, HKB constitutes the foundation of a mechanistic science of coordination called Coordination Dynamics that extends from matter to movement to mind, and beyond. [ABSTRACT FROM AUTHOR]

Human interaction partners tend to synchronize their movements during repetitive actions such as walking. Research of inter-human coordination in purely rhythmic action tasks reveals that the observed patterns of interaction are dominated by synchronization effects. Initiated by our finding that human dyads synchronize their arm movements even in a goal-directed action task, we present a step-wise approach to a model of inter-human movement coordination. In an experiment, the hand trajectories of ten human dyads are recorded. Governed by a dynamical process of phase synchronization, the participants establish in-phase as well as anti-phase relations. The emerging relations are successfully reproduced by the attractor dynamics of coupled phase oscillators inspired by the Kuramoto model. Three different methods on transforming the motion trajectories into instantaneous phases are investigated and their influence on the model fit to the experimental data is evaluated. System identification technique allows us to estimate the model parameters, which are the coupling strength and the frequency detuning among the dyad. The stability properties of the identified model match the relations observed in the experimental data. In short, our model predicts the dynamics of inter-human movement coordination. It can directly be implemented to enrich human-robot interaction. [ABSTRACT FROM AUTHOR]

The dynamics of rhythmic movement has both deterministic and stochastic features. We advocate a recently established analysis method that allows for an unbiased identification of both types of system components. The deterministic components are revealed in terms of drift coefficients and vector fields, while the stochastic components are assessed in terms of diffusion coefficients and ellipse fields. The general principles of the procedure and its application are explained and illustrated using simulated data from known dynamical systems. Subsequently, we exemplify the method’s merits in extracting deterministic and stochastic aspects of various instances of rhythmic movement, including tapping, wrist cycling and forearm oscillations. In particular, it is shown how the extracted numerical forms can be analysed to gain insight into the dependence of dynamical properties on experimental conditions. [ABSTRACT FROM AUTHOR]

Abstract. Most studies of movement coordination deal with temporal patterns of synchronization between components, often without regard to the actual amplitudes the components make. When such a system is required to produce a composite action that is spatially constrained, coordination persists, but its stability is modulated by spatial requirements effected, we hypothesize, through the component amplitudes. As shown experimentally in part I, when a redundant three-joint system (wrist, elbow, and shoulder) is required to trace a specified arc in space, the joint angles may be frequency- and phased-locked even as the curvature of the trajectory is manipulated. Transitions between joint coordination patterns occur at a critical curvature, accompanied by a significant reduction in wrist amplitude. Such amplitude reduction is viewed as destabilizing the existing coordinative pattern under current task constraints, thereby forcing the joints into a more stable phase relationship. This paper presents a theoretical analysis of these multijoint patterns and proposes an amplitude mechanism for the transition process. Our model uses three linearly coupled, nonlinear oscillators for the joint angles and reproduces both the observed interjoint coordination and component amplitude effects as well as the resulting trajectories of the end effector. [ABSTRACT FROM AUTHOR]