A theoretical framework based on the concepts and tools of nonlinear dynamical systems is advanced to account for both the persistent and transitory changes traditionally shown for the learning and development of motor skills. The multiple time scales of change in task outcome over time are interpreted as originating from the system's trajectory on an evolving attractor landscape. Different bifurcations between attractor organizations and transient phenomena can lead to exponential, power law, or S-shaped learning curves. This unified dynamical account of the functions and time scales in motor learning and development offers several new hypotheses for future research on the nature of change in learning theory.

We present first numerical evidence that in an excitable medium the synchronization of spatiotemporal patterns with external excitatory waves shows a sharp peak at a finite, well-defined noise level independent of the system size. This effect can be understood as a generalization of the concept of stochastic resonance to spatially extended systems. We further show the impact of spatiotemporal stochastic resonance for the spreading of spiral waves, where the noise level controls the scale and size of the spiral. 05.40.+j, 47.54.+r Pattern formation far from equilibrium has been studied very extensively in the last years (for a recent review, see [1,2]). Representative examples are Rayleigh-Benard convection rolls, Taylor-Couette flow, and spiral waves in the Belousov-Zhabotinsky reaction. Typically a pattern starts to build up when the control parameter (the temperature difference in case of the Rayleigh-Benard system) becomes larger than a critical value. Noise makes the bifurcation smooth by triggering the onset of the pattern even below threshold r ( r, . The role of fluctuations for the onset and selection of patterns has been studied in some detail and is reported on in a number of articles in [3,4] and [5]. In this paper, we discuss the role of noise for the formation of patterns in two-dimensional excitable media from a different perspective.It has been shown that a certain amount of noise can amplify temporal patterns by increasing the system's sensitivity via stochastic resonance [6] (for recent reviews, see [7,8]). This effect has been shown first for symmetric bistable systems. The external forcing (the temporal pattern) tilts the bistable potential weakly back and force (weak enough that the potential remains bistable), thereby modulating the barrier height for noise-induced hopping between the stable domains. The synchronization of the hopping with the external forcing shows a bell-shaped curve as a function of the noise strength -the fingerprint of stochastic resonance. Only recently, stochastic resonance has been demonstrated in much simpler systems, namely in threshold devices [9 -11]. Here, Gaussian noise and a periodic signal is applied to a threshold device which responds with a spike if the sum of the noise and the signal is crossing the threshold from below. The intensity of the peak at the signal frequency in the power spectrum of the outgoing spike train shows a bell-shaped curve as a function of the variance of the noise. At the maximum, the variance of the noise matches half the square of the threshold -a result which we will make heavy use of in this paper. The basic question we study in this paper is in how far stochastic resonance can also be observed in spatially extended pattern forming systems. As a working model, we use a two-dimensional equidistant square array (lattice constant a) of N X N noisy threshold devices [9] d;, : x;, (t)~s;, (t) (i = 1, ... , N and j = 1, ... , N). The operation of a threshold device is defined as follows: If the input x;, (t) is below the threshold...

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The experiments examined qualitative and quantitative changes in the dynamics of learning a novel motor skill (roller ball task) as a function of the manipulation of a control parameter (initial ball speed). The focus was on the relation between the rates of change in performance over practice time and the changing time scales of the evolving attractor dynamic. Results showed 3 different learning patterns to the changes in the dynamics as a function of practice that were mediated by the initial ball speed. Only participants who learned the task showed a bifurcation in coordination mode that was preceded by enhanced performance variability. The observed multiple time scales to motor learning are interpreted as the products of the dynamical stability and instability realized from (a) the continually evolving landscape dynamics due to bifurcations between attractor organization and (b) the transient phenomena associated with moving toward and away from fixed-point dynamics.

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A I 9iaJuI pul pusG Ua L99G I gul 19 91cal Information Center is to provide the broadest dissemination possible of information contained in DOE's Research and Development Reports to business, industry, the academic community, and federal, state and local governments, Although a small portion of this report is not reproducible, it is being made available to expedite the availability of information on the research discussed herein.

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