The use of (symmetry) group theory as a predictive tool for studying bimanual coordination.

Symmetry groups-rules that connect different configurations of a given set of components-represent a compact means of coding for effects, a feature that is desirable in both model- and theory-building. The present study was designed to compare the effects of spatial orientation differences with the various other asymmetries (e.g., timing differences, handedness preferences, the direction of attention) that are accommodated by current models of bimanual coordination. The authors used symmetry groups to predict specific patterns of results. In 2 experiments, participants (N = 13, Experiment 1; N = 9, Experiment 2) coordinated the movements of differently oriented (1 downward and 1 upward) pendulum pairs at a low (0.62 Hz) or high (0.82 Hz) movement frequency to establish an in-phase or antiphase pattern. Consistent with previous results (P. G. Amazeen, E. L. Amazeen, & M. T. Turvey, 1998a), the downward-oriented pendulum tended to lead slightly. In contrast to the effects of other bimanual asymmetries, the downward-oriented pendulum lead was amplified at low frequencies. Although the results contradicted the predictions of existing models of bimanual coordination, they were consistent with predictions from symmetry group theory. In the discussion, the authors focus on the application of symmetry groups to both bimanual coordination and other phenomena with more complex symmetric structures.

Coupling of breathing and movement during manual wheelchair propulsion.

The hypothesis of this study was that stable coordination patterns may be found both within and between physiological subsystems. Many studies have been conducted on both monofrequency and multifrequency coordination, with a focus on both the frequency and phase relations among the limbs. In the present study, locomotor-respiratory coupling was observed in the maintenance of small-integer frequency ratios (2:1, 3:1, and 4:1) and in the consistent placement of the inspiratory phase just after the onset of the movement cycle during wheelchair propulsion. Level of experience and various motor and respiratory parameters were manipulated. Coupling was observed across levels of experience. Increases in movement frequency were accompanied by a shift to larger-integer ratios, suggesting that a single modeling strategy (e.g., the Farey tree; D. L. González & O. Piro, 1985) may be used for coordination both within the motor subsystem and between it and other physiological subsystems.

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. For both kinds of coordination, the steady state and breakdown of bimanual rhythmic coordination as indexed by the time series of the relative phase angle phi were studied under the manipulation of coordination mode, frequency of oscillation, and the difference in the eigenfrequencies (preferred tempos) of the individual oscillating limbs. The properties observed for both intra- and interpersonal coordination were those predicted by a dynamical model of rhythmic coordination that considers the coordinated limbs coupled to be nonlinear oscillators. Using a regression method, the coupling strengths of the coupled system were recovered. As predicted by the dynamical model, the strength of the dynamic was generally greater for the in-phase than the anti-phase mode and decreased with increasing frequency. Further, the strength of the interpersonal interlimb coupling was weaker than that of intrapersonal interlimb coupling.

Breaking the reflectional symmetry of interlimb coordination dynamics.

Interlimb rhythmic coordination is reflectionally symmetric when the left and right limb segments are identical in uncoupled frequencies and spatial orientation. In the present studies (4 experiments, with a total of 31 participants), when reflectional symmetry was broken through differences in timing (frequency), the resulting stable states were related by reflection and were identical for paired identically oriented limb segments behaving either as inverted or as ordinary pendulums. When reflectional symmetry was broken both temporally and spatially (coordinating inverted and ordinary pendular motions), the resulting stable states were different from those produced by identically oriented pendulums but nevertheless were related by reflection. In the Discussion, the authors focus on (a) symmetry breaking as leading to one of a number of symmetrically related states and (b) extending coordination dynamics with reflectional symmetry so that temporal and spatial asymmetries can both be accommodated.

Frequency detuning of the phase entrainment dynamics of visually coupled rhythmic movements.

An order parameter equation for correlated limb movements was applied to rhythmic coordination between the limbs of two people. The interlimb coordination was established and maintained through vision. Manipulations of frequency competition, coupled frequency, and intended mode (in-phase or anti-phase) produced equilibria and fluctuations in relative phase predicted by the order parameter equation and confirmed originally in within-person coordination. It was concluded that there is an elementary coordination dynamics governing the rhythmic coordination between organisms as well as between components of a single organism.