Organization of Compensatory Postural Coordination Patterns

The authors investigated whether compensatory postural coordination patterns are organized according to the same dynamical principles as are nonequilibrium phase transitions. Eight participants were asked to maintain upright balance on a moving platform that was sinusoidally translated in the anterior-posterior direction and was systematically increased and decreased 0.19 Hz as a step function every 10 platform cycles through the frequency range 0.19–1.46 Hz. At low platform frequencies, all participants exhibited small joint angular motions with high variability, and the relative phase between the joint motions exhibited drifting patterns and large fluctuations. As platform frequency increased, the amplitude of joint motion increased systematically and joint-specific oscillatory patterns emerged. The findings provided no evidence for a Hopf bifurcation or hysteresis in the transitions of postural coordination modes, however, or, mote generally, a basis for distinguishing the relevance of linear versus nonlinear models of postural control.     

Organization of compensatory postural coordination patterns

The authors investigated whether compensatory postural coordination patterns are organized according to the same dynamical principles as are nonequilibrium phase transitions. Eight participants were asked to maintain upright balance on a moving platform that was sinusoidally translated in the anterior-posterior direction and was systematically increased and decreased 0.19 Hz as a step function every 10 platform cycles through the frequency range 0.19-1.46 Hz. At low platform frequencies, all participants exhibited small joint angular motions with high variability, and the relative phase between the joint motions exhibited drifting patterns and large fluctuations. As platform frequency increased, the amplitude of joint motion increased systematically and joint-specific oscillatory patterns emerged. The findings provided no evidence for a Hopf bifurcation or hysteresis in the transitions of postural coordination modes, however, or, more generally, a basis for distinguishing the relevance of linear versus nonlinear models of postural control.     

Self-organization of coordinative movement patterns

We present a strictly operational approach — in which theoretical tools and experimental data are developed together — to the problem of understanding the coordination of movement patterns. The empirical aspects are guided by synergetics, a theory of spontaneous pattern formation in open systems. Following an outline of our theoretical strategy, recent experimental results are reviewed that demonstrate the validity of the approach. From these studies, it is possible to establish the linkage between order-order transitions in movement behavior and other nonequilibrium phase transitions in nature. Behavioral patterns (corresponding to low-dimensional attractors for collective variables) and their dynamics are shown to arise in a purely self-organized fashion from cooperative coupling among individual components. This step has been implemented analytically and computationally. The insights gained from the present research allow a generalization in the form of seven theoretical propositions that aim at characterizing pattern formation, stability and change in complex, biological systems. In turn, a number of new research directions emerge, including studies of the collective dynamics of the environment-movement system, learning, and multiple-limb coordination.     

Interpersonal dynamics in sport: The role of artificial neural networks and 3-D analysis

In previous attempts to identify dynamical systems properties in patterns of play in team sports, only 2-D analysis methods have been used, implying that the plane of motion must be preselected and that movements out of the chosen plane are ignored. In the present study, we examined the usefulness of 3-D methods of analysis for establishing the presence of dynamical systems properties, such as phase transitions and symmetry-breaking processes in the team sport of rugby. Artificial neural networks (ANN s) were employed to reconstruct the 3-D performance space in a typical one-versus-one subphase of rugby. Results confirm that ANs are reliable tools for reconstructing a 3-D performance space and may be instrumental in identifying pattern formation in team sports generally.     

Cortical coordination dynamics and cognition

New imaging techniques in cognitive neuroscience have produced a deluge of information correlating cognitive and neural phenomena. Yet our understanding of the inter-relationship between brain and mind remains hampered by the lack of a theoretical language for expressing cognitive functions in neural terms. We propose an approach to understanding operational laws in cognition based on principles of coordination dynamics that are derived from a simple and experimentally verified theoretical model. When applied to the dynamical properties of cortical areas and their coordination, these principles support a mechanism of adaptive inter-area pattern constraint that we postulate underlies cognitive operations generally.     

Effects of velocity and limb loading on the coordination between limb movements during walking

The authors investigated the effects of velocity (increasing from 0.5 to 5.0 km/hr in steps of 0.5 km/hr) and limb loading on the coordination between arm and leg movements during treadmill walking in 7 participants. Both the consistency of the individual limb movements and the stability of their coordination increased with increasing velocity; the frequency coordination between arm and leg movements was 2:1 at the lower velocities and 1:1 at the higher velocities. The mass manipulation affected the individual limb movements but not their coordination, indicating that a stable walking pattern was preserved. The results differed qualitatively from those obtained in studies on bimanual interlimb coordination, implying that the dynamical principles identified therein are not readily applicable to locomotion.     

Phase Transitions and Critical Fluctuations in Rhythmic Coordination of Ipsilateral Hand and Foot

Four subjects performed rhythmic movements of the ankle and the wrist in time with an auditory metronome, in two modes of coordination, antiphase and in-phase. The forearm was placed in either a prone or a supine position. When movements were prepared in the antiphase mode, spontaneous transitions to the in-phase mode, or to phase wandering were observed as metronome frequency was increased. When prepared in the in-phase mode, transitions between in-phase modes or to phase wandering were occasionally observed. Predicted signature features of nonequilbrium phase transitions were noted, including loss of stability and critical fluctuations. The stability of the movement patterns was determined by spatial (dependent upon the direction of movement) rather than anatomical (dependent on the coupling of specific muscle groups) constraints. The position of the forearm had no consistent bearing upon the variability of the phase relations between the limbs, the frequency of phase transitions, or the time of onset of transitions. These results are discussed with reference to the coordination dynamics (e.g., multistability, loss of stability) of multijoint movements.     

Perspective-taking in dialogue as self-organization under social constraints

We present a dynamical systems account of how simple social information influences perspective-taking. Our account is motivated by the notion that perspective-taking may obey common dynamic principles with perceptuomotor coupling. We turn to the prominent HKB dynamical model of motor coordination, drawing from basic principles of self-organization to describe how conversational perspective-taking unfolds in a low-dimensional attractor landscape. We begin by simulating experimental data taken from a simple instruction-following task, in which participants have different expectations about their interaction partner. By treating belief states as different values of a control parameter, we show that data generated by a basic dynamical process fits overall egocentric and other-centric response distributions, the time required for participants to enact a response on a trial-by-trial basis, and the action dynamics exhibited in individual trials. We end by discussing the theoretical significance of dynamics in dialog, arguing that high-level coordination such as perspective-taking may obey similar dynamics as perceptuomotor coordination, pointing to common principles of adaptivity and flexibility during dialog.     

Evolution of behavioral attractors with learning: nonequilibrium phase transitions.

Learning a bimanual coordination task (synchronization to a visually specified phasing relation) was studied as a dynamical process over 5 days of practicing a required phasing pattern. Systematic probes of the attractor layout of the 5 Ss' coordination dynamics (expressed through a collective variable, relative phase) were conducted before, during, and after practice. Depending on the relationship between the initial coordination dynamics (so-called intrinsic dynamics) and the pattern to be learned (termed behavioral information, which acts as an attractor of the coordination dynamics toward the required phasing), qualitative changes in the phase diagram occurred with learning, accompanied by quantitative evidence for loss of stability (phase transitions). Such effects persisted beyond 1 week. The nature of change due to learning (e.g., abrupt vs. gradual) is shown to arise from the cooperative or competitive interplay between behavioral information and the intrinsic dynamics.     

Postural coordination modes considered as emergent phenomena.

The coordination of multiple body segments (torso and legs) in the control of standing posture during a suprapostural task was studied. The analysis was motivated by dynamical theories of motor coordination. In 2 experiments it was found that multisegment postural coordination could be described by the relative phase of rotations around the hip and ankle joints. The effective length of the feet, the height of the center of mass, and the amplitude of head motions in a visual tracking task were varied. Across these variations, 2 modes of hip-ankle coordination were observed: in-phase and anti-phase. The emergence of these modes was influenced by constraints imposed by the suprapostural tracking task, supporting the idea that such tasks influence postural control in an adaptive manner. Results are interpreted in terms of a dynamical approach to coordination in which postural coordination modes can be viewed as emergent phenomena.     

Diffusive,Synaptic, and Synergetic Coupling: An Evaluation Through In-Phase and Antiphase Rhythmic Movements

The in-phase and antiphase patterns of interlimb l:1 frequency locking were contrasted with respect to models of coordination dynamics in biological movement systems that are based on diffusive coupling, synaptic coupling, and synergetic principles. Predictions were made from each model concerning the stable relative phase phi between the rhythmic units, its standard deviation SDphi and the self-chosen coupled frequency omegasubc;. The experimental task involved human subjects oscillating two handheld pendulums either in-phase or antiphase. The eigenfrequencies of the two hand-pendulum systems were manipulated by varying the length and mass of each pendulum individually. Relative to an eigenfrequency difference of Delta equal to zero, |Deltaomega| > 0 displaced phi from phi = 0 and phi = pi, and amplified SDphi. omegasubc; decreased with |Deltaomega|. Both the displacement of phi and SDphi were greater in the antiphase mode. Additionally, the displacement of phi increased more sharply with |Delta| for antiphase than for in-phase coordination. In contrast, omegasubc; was identical for the two coordination modes. Of the models of interlimb coordination dynamics, the synergetic model was the most successful in addressing the pattern of dependencies of phi and SDphi. The specific forms of the functions relating omegasubc; and phi to Deltaomega pose challenges for all three models, however     

Bimanual Finger Tapping: Effects of Frequency and Auditory Information on Timing Consistency and Coordination

The authors' goal in this study was to probe the basis for an earlier, unexpected finding that preferred-frequency finger tapping tends to have higher frequencies and to be less stable for in-phase than for antiphase tasks. In follow-up experiments, 3 protocols were employed: a preferred-frequency replication in both coordination modes, a metronome-driven matching of the preferred frequencies to each of the coordination modes, and a frequency scaling of both modes. The original findings were affirmed for preferred frequency. Tapping to a metronome had a differential effect on in-phase and antiphase: A more stable coupling across frequencies was exhibited during in-phase. Under frequency scaling, the antiphase pattern decomposed at lower frequencies than did in-phase, but no phase transitions were observed. The loss of stable coordination in both modes was attended by sudden increases in frequency differences between fingers and by phase wandering. The emergence of those effects is discussed in light of asymmetric modifications to the Haken-Kelso-Bunz model (H. Haken, J. A. S. Kelso, & H. Bunz, 1985) and the task constraints of tapping.     

Bimanual finger tapping: effects of frequency and auditory information on timing consistency and coordination

The authors' goal in this study was to probe the basis for an earlier, unexpected finding that preferred-frequency finger tapping tends to have higher frequencies and to be less stable for in-phase than for antiphase tasks. In follow-up experiments, 3 protocols were employed: a preferred-frequency replication in both coordination modes, a metronome-driven matching of the preferred frequencies to each of the coordination modes, and a frequency scaling of both modes. The original findings were affirmed for preferred frequency. Tapping to a metronome had a differential effect on in-phase and antiphase: A more stable coupling across frequencies was exhibited during in-phase. Under frequency scaling, the antiphase pattern decomposed at lower frequencies than did in-phase, but no phase transitions were observed. The loss of stable coordination in both modes was attended by sudden increases in frequency differences between fingers and by phase wandering. The emergence of those effects is discussed in light of asymmetric modifications to the Haken-Kelso-Bunz model (H. Haken, J. A. S. Kelso, & H. Bunz, 1985) and the task constraints of tapping.     

Structures,dynamics and mechanisms in neuroscience: an integrative account

Proponents of mechanistic explanations have recently proclaimed that all explanations in the neurosciences appeal to mechanisms. The purpose of the paper is to critically assess this statement and to develop an integrative account that connects a large range of both mechanistic and dynamical explanations. I develop and defend four theses about the relationship between dynamical and mechanistic explanations: that dynamical explanations are structurally grounded, that they are multiply realizable, possess realizing mechanisms and provide a powerful top-down heuristic. Four examples shall support my points: the harmonic oscillator, the Haken–Kelso–Bunz model of bimanual coordination, the Watt governor and the Gierer–Meinhardt model of biological pattern formation. I also develop the picture of “horizontal” and “vertical” directions of explanations to illustrate the different perspectives of the dynamical and mechanistic approach as well as their potential integration by means of intersection points.     

Asymmetries in Coupling Dynamics of Perception and Action

The influence of information-based dynamics on coordination dynamics of rhythmic movement was examined with special reference to the expression of asymmetries. In Experiment 1, right-handed subjects performed unimanual, rhythmical movements in coordination with either a discrete or continuous visual display. The right hand-visual display system defined a more stable perception-action collective than the left, particularly when continuous visual information was available. In Experiment 2, the same subjects performed rhythmic bimanual movements in coordination with a continuous visual display. The action collective was inherently more stable than the perception-action collective, although similar patterns were observed at both levels. Importantly, the dynamics of the perception-action collective impinged upon the dynamics of the action collective in terms of stability. Asymmetries remained evident between limbs in the bimanual preparations, with the left hand exhibiting greater limit-cycle variability and also a tendency to more often effect transitions at the action couple. Features of dynamical models that capture characteristics of manual asymmetries are discussed.     

The interplay of attention and bimanual coordination dynamics

Despite their common origin, studies on motor coordination and on attentional load have developed into separate fields of investigation, bringing out findings, methods, and theories which are diverse if not mutually exclusive. Sitting at the intersection of these two fields, this article addresses the issue of behavioral flexibility by investigating how intention modifies the stability of existing patterns of coordination between moving limbs. It addresses the issue, largely ignored until now, of the attentional cost incurred by the central nervous system (CNS) in maintaining a coordination pattern at a given level of stability, in particular under different attentional priority requirements. The experimental paradigm adopted in these studies provides an original mix of a classical measure of attentional load, namely, reaction time, and of a dynamic approach to coordination, most suitable for characterizing the dynamic properties of coordinated behavior and behavioral change. Findings showed that central cost and pattern stability covary, suggesting that bimanual coordination and the attentional activity of the CNS involved in maintaining such a coordination bear on the same underlying dynamics. Such a conclusion provides a strong support to a unified approach to coordination encompassing a conceptualization in terms of information processing and another, more recent framework rooted in self-organization theories and dynamical systems models     

Disentangling stability, variability and adaptability in human performance: focus on the interplay between local variance and serial correlation

We address the complex relationship between the stability, variability, and adaptability of psychological systems by decomposing the global variance of serial performance into two independent parts: the local variance (LV) and the serial correlation structure. For two time series with equal LV, the presence of persistent long-range correlations (or 1/? β noise) increases the global variance. We hypothesized that a coadjustment between these two determinants of variability constitutes a resource for adaptive systems whose appropriate functioning under critical conditions requires the outcome variance to be limited. To test this hypothesis, we looked at the bimanual coordination dynamics at comfortable (stable) and critical (close to phase transition) frequencies. Results showed that a negative correlation appeared gradually as the theoretical stability of coordination modes decreased and reached significance only in the critical condition. We propose that the emergence of a mutual adjustment between LV and serial correlations might be an indicator of effective adaptation to stabilize behavior.     

Phase transitions and critical fluctuations in the visual coordination of rhythmic movements between people

By watching each other's lower oscillating leg, 2 seated Ss kept a common tempo and a particular phase relation of either 0 degrees (symmetric mode) or 180 degrees (alternate mode). This study investigated the differential stability of the 2 phase modes. In Experiment 1, in which Ss were instructed to remain in the initial phase mode, the alternate phase mode was found to be less stable as the frequency of oscillation increased. In addition, analysis of the nonsteady state cycles revealed evidence of a switching to the symmetric phase mode for the initial alternate phase mode trials. In Experiments 2 and 3, Ss were instructed to remain at a noninitial phase angle if it was found to be more comfortable. The transition observed between the 2 phase modes satisfies the criteria of a physical bifurcation--hysteresis, critical fluctuations, and divergence--and is consonant with previous findings on transitions in limb coordination within a person.