A.A. Post

Relative phase dynamics in perturbed interlimb coordination: stability and stochasticity

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, anti-phase) 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, noise strength Q did not vary as a function of movement frequency. However, systematic differences in Q were observed between the two coordination modes. The advantages and (potential) pitfalls of using stationary performance of single patterns to examine the stability features of a bistable potential were discussed.

Relative phase dynamics in perturbed interlimb coordination: the effects of frequency and amplitude

Abstract. Schöner [Schöner 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 anti-phase 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 (relative) timing level are affected only moderately by task constraints pertaining to the goal level, and that models of interlimb coordination in which amplitude coupling plays a partial or subordinate role should be preferred above models relying solely on amplitude coupling.

Timing the selection of information during rhythmic catching

Catching a ball requires that information be available close to the catch but early enough for prospective or corrective control. In the present experiment, 6 participants were asked to throw and catch a ball continuously for 1 min while wearing liquid-crystal goggles that restricted viewing to specific amounts of time at specific intervals. Participants were free to select the information by varying the frequency and phasing of throwing relative to the goggles. Video analysis revealed that they elected a frequency of throwing that matched the goggle frequency and chose to view the ball at or around its zenith. Earlier portions of the balls trajectory were viewed as the goggle frequency increased. Despite variations in the viewing location, participants elected to view the ball on average 365 ms before the catch. Analysis of the hands trajectory further revealed that the time interval (M = 82 ms) between the balls zenith and the initiation of the final motion of the hand toward the catch did not vary as a function of the frequency of throwing. The authors conclude that the timing constraints imposed by the hands movement are the basis for the selection of information for catching.

Effects of visual information and task constraints on intersegmental coordination in playground swinging

Abstract The authors investigated how and to what extent visual information and associated task constraints are negotiated in the coordinative structure of playground swinging. Participants (N = 20) were invited to pump a swing from rest to a prescribed maximal amplitude under 4 conditions: normal vision, no vision, and 2 visual conditions involving explicit phasing constraints. In the latter conditions, participants were presented with a flow pattern consisting of a periodically expanding and contracting optical structure. They were instructed to phase the swing motion so that the forward turning point coincided with either the maximal size (enhanced optical flow) or the minimal size (reduced optical flow) of the presented flow pattern. Removal of visual information clearly influenced the swinging behavior, in that intersegmental coordination became more stereotyped, reflecting a general stiffening of the swinger. The conditions involving explicit phasing requirements also affected the coordination, but in an opposite way: The coordination became less stereotyped. The two phasing instructions had differential effects: The intersegmental coordination deviated more from normal swinging (i.e., without phasing constraints) when optical flow was enhanced than when it was reduced. Collectively, those findings show that visual information plays a formative role in the coordinative structure of swinging, in that variations of visual information and task constraints were accompanied by subtle yet noticeable changes in intersegmental coordination.