Why do humans switch from walking to running at a particular speed? It is proposed that gait transitions behave like nonequilibrium phase transitions between attractors. Experiment 1 examined walking and running on a treadmill while speed was varied. The transition occurred at the equal-energy separatrix between gaits, with predicted shifts in stride length and frequency, a qualitative reorganization in the relative phasing of segments within a leg, a sudden jump in relative phase, enhanced fluctuations in relative phase, and hysteresis. Experiment 2 dissociated speed, frequency, and stride length to show that the transition occurred at a constant speed near the energy separatrix. Results are consistent with a dynamic theory of locomotion in which preferred gaits are characterized by stable phase relationships and minimum energy expenditure, and gait transitions by a loss of stability and the reduction of energetic costs.Motor behavior in humans and animals exhibits two notable features: the presence of stable patterns of coordination and the sudden reorganization that occurs when switching between them. Much research has been directed at describing individual motor patterns such as walking and reaching, but the study of behavioral transitions may reveal principles of the formation of coordinative patterns. Locomotion offers a model system for the study of both, for it is a fundamental, fluent, and complex behavior that is likely to share basic characteristics with other skilled actions. In this article, we examine the shift between walking and running in humans and offer a qualitative dynamic theory of gait transitions.As speed increases, humans and other animals shift from a walking gait to a running gait at a characteristic speed. Why does this occur? A common view is that each gait is orchestrated by a central motor plan, such as a motor program or spinal pattern generator, and that gait transitions simply involve switching between plans (e.g., Shapiro, Zernicke, Gregor, & Diestel, 1981). This view does not offer predictions about the details of behavior at gait transitions. By contrast, we propose that gait transitions are a consequence of the intrinsic dynamics of a complex system, with properties characteristic of bifurcations between attractors. We show that the walk-run (W-R) transition exhibits features of a nonequilibrium phase transition and that it occurs at a speed that tends to reduce energetic costs. This

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In this paper, we examine how infants' natural manual and postural activities ± what they prefer and do week by week ± are related to developmental transitions in reaching skill and its neuromuscular control. Using a dense, longitudinal design, we tracked the manual and postural activities of four infants in a natural, free-play setting across the first year of life, and related these activities to two transitions in reaching as measured in a structured laboratory setting: the transition to reaching and the transition to stable reaching. Our data indicated that specific advances in the free-play setting preceded both transitions. Head and upper torso control, the ability to extend the arm and hand to a distant target, and the ability to touch and grasp objects placed nearby were all precursors to the onset of reaching, whereas sitting independently was associated with the transition to stable reaching. We also found important individual variability in when these`components' were in place, indicating that it is the ensemble of components that is essential, not the order in which they develop or the timing of their contribution. These findings suggest that subsequent experimental manipulations should be planned with respect to infants' individual constellations of skills, rather than looking at only a single precursor to change.

Why do infants make perseverative errors when reaching for two identical targets? From a dynamic systems perspective, perseverative errors emerge from repetitive perceptual ±motor activity in novel andaor difficult contexts. To evaluate this account, we studied 9-month-old infants performing two tasks in which they repetitively reached toward either a single target or two identical targets. Results showed that, in the context of the two identical targets, perseverative responses were preceded by the creation of strong memories of previous reach directions and trajectories. In contrast, we found little evidence for convergence on habitual reach trajectories when the infants performed the less taxing singletarget task, suggesting that the demands of reaching for two identical targets strongly constrained the reaching behavior. In total, results indicated that memories of prior movements make a critical contribution to performance in the A-not-B task and its variants.

Skilled behavior requires a balance between previously successful behaviors and new behaviors appropriate to the present context. We describe a dynamic field model for understanding this balance in infant perseverative reaching. The model predictions are tested with regard to the interaction of two aspects of the typical perseverative reaching task: the visual cue indicating the target and the memory demand created by the delay imposed between cueing and reaching. The memory demand was manipulated by imposing either a 0-or a 3-second delay, and the salience of the cue to reach was systematically varied. Infants demonstrated fewer perseverative errors at 0-delay versus 3-second delay based on the cue salience, such that a more salient visual cue was necessary to overcome a longer delay. These results have important implications for understanding both the basic perceptualmotor processes that produce reaching in infants and skilled flexible behavior in general.

Diedrich and Warren (1995a) proposed that gait transitions behave like bifurcations between attractors, with the relative phase of the leg segments as an order parameter and stride frequency and stride length as control parameters. In the present experiments, the authors tested the prediction that manipulation of the attractor layout, either through the addition of load to the ankles or through an increase in the grade of the treadmill, induces corresponding changes in the walk-run transition. As predicted, the load manipulation shifted the most stable walk and the transition to lower stride frequencies. In contrast, the grade manipulation shifted the most stable walk and the transition to shorter stride lengths. Other features of the dynamic theory were also replicated, including enhanced fluctuations of phase and systematic changes in stride length and frequency at the transition. Overall, in these experiments a shift of the attractors in control parameter space yielded a corresponding shift of the transition.

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How one selects a movement when faced with alternative ways of doing a task is a central problem in human motor control. Moving the fingertip a short distance can be achieved with any of an infinite number of combinations of knuckle, wrist, elbow, shoulder, and hip movements. The question therefore arises: how is a unique combination chosen? In our model, choice is achieved by consideration of the similarity between the task requirements and the optimal biomechanical performance of each limb segment. Two variants of the model account for the movements that are selected when subjects freely oscillate the fingertip and when they tap against an obstacle. An important feature of both is that the impulse of collision with an obstacle (as in drumming with the hand or tapping with the finger) is assumed to be controlled in part by aiming for a point beyond the surface being struck. Thus, a force-related control variable may be represented and controlled spatially.