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G Schöner

Publications and source records attributed to G Schöner.

31 records · Page 2Linked to original sources
PubMed1993

Dynamic properties of cortical evoked (10 Hz) oscillations: theory and experiment.

Experiments probed the dynamic properties of stimulus-evoked (approximately 10 Hz) oscillations in somatosensory cortex of anesthetized rats. Experimental paradigms and statistical time series analysis were based on theoretical ideas from a dynamic approach to temporal patterns of neuronal activity. From the results of a double-stimulus paradigm we conclude that the neuronal response contains two components with different dynamics and different coupling to the stimulus. Based on this result a quantitative dynamic model is derived, making use of normal form theory for bifurcating vector fields. The variables used are abstract, but measurable, dynamic components. The model parameters capture the dynamic properties of neuronal response and are related to experimental results. A structural interpretation of the model can be given in terms of the collective dynamics of neuronal groups, their mutual interaction, and their coupling to peripheral stimuli. The model predicts the stimulus-dependent lifetime of the oscillations as observed in experiment. We show that this prediction relies on the basic concept of dynamic bistability and does not depend on the modeling details.

Animals↗
PubMed1992

Learning as change of coordination dynamics: theory and experiment.

Learning of coordination patterns was investigated theoretically from the point of view of a dynamic theory of biological coordination and with reference to recent experiments on the learning of relative timing patterns. The theory is based on theoretical and experimental work showing that coordinated movement is characterized not only by the actually performed pattern of coordination but by an entire dynamics of coordination. Theoretically, such dynamics are captured as equations of motion of relevant collective variables. Experimentally, signatures of these underlying dynamics can be found in the temporal stability of coordination patterns, which can be assessed through various stability measures as well as through processes of pattern change. We argue that not only intrinsic coordination tendencies, but also specific behavioral requirements, be they perceived, memorized, or intended, must be expressed in terms of such dynamics. The concept of behavioral information captures such requirements as part of the coordination dynamics. We expound two hypotheses on the nature of learning in this framework. First, we assume that at each point during the learning process the system is governed by a well-defined coordination dynamics. This equation of motion evolves with learning so as to acquire an attractor solution near the to-be-learned pattern. Second, we hypothesize that this change of the coordination dynamics, captured by the time course of memorized behavioral information, can itself be ascribed to an additional layer of dynamics, the slower learning dynamics. Testable consequences of these views are discussed in the light of recent experimental findings on the learning of a relative phase in rhythmic movement: (a) Learning affects dynamic properties of performed coordination patterns, in particular, their stability; (b) the change of the coordination dynamics due to learning leads to specific changes of behavior also under conditions other than the learned condition, namely, to systematic deviation toward the learned patterns; (c) learning may lead to instabilities in the coordination behavior if initial and learned performance differ sufficiently; and (d) the dynamic properties of the performed coordination patterns are distinct on the two time scales of learning and of performance.

Journal Article↗
PubMed1992

Evoked oscillatory cortical responses are dynamically coupled to peripheral stimuli.

We report that the response of neurons in rat somatosensory cortex to tactile stimulation consists of two components, a short-latency response and an oscillatory response, observable as up to 8 peaks in the post-stimulus-time-histogram with interpeak intervals in the order of 100 ms (10 Hz). While the first component is always stimulus locked, the second component is strictly stimulus-locked only when elicited from the resting state: once started, the oscillations are only weakly affected by further stimulation. This implies generally that the question of stimulus locking of oscillatory response components is not a yes/no question. Instead, the concept of dynamic coupling is shown to adequately capture the different limit cases. We present a simple dynamic model that exemplifies this point.

Animals↗
PubMed1991

Dynamic theory of action-perception patterns: the "moving room" paradigm.

Action-perception patterns are studied theoretically in terms of equations of motion that capture the coordination capacity of the nervous system. We consider intrinsic dynamics in the absence of visual information that contain a single posture state as a fixed point attractor. We couple these intrinsic dynamics to visual information that stabilizes posture in the visual world. This leads to a theory of postural sway induced by an optic flow field ("moving room" paradigm). The optic flow is parametrized in a simplest approximation by the expansion rate of a relevant perceptual target. We show how temporal stability as the key concept of this theory can lead to prediction and serve as a measure of perceptual coupling. Finally, we discuss the relation of the present theory to biological cybernetics.

Animals↗
PubMed1990

A synergetic theory of quadrupedal gaits and gait transitions.

We present a theoretical analysis of the patterns of interlimb co-ordination in the gaits of quadrupedal locomotion. Introducing as collective variables a set of relative phases that describe the co-ordination patterns, we classify gaits by their symmetry properties, which can be expressed as invariances under groups of transformations. We define dynamics of the collective variables, on which we impose symmetry restrictions. The stable observable gait patterns correspond to atractors of these dynamics. A non-trivial consequence of this theoretical viewpoint is that gait transitions can take the form of non-equilibrium phase transitions that are accompanied by loss of stability. We show how various types of such phase transitions involving hysteresis, slowing down and fluctuation enhancement can occur. Also the difference between smooth and abrupt transitions is given theoretical foundation. While existing experimental evidence is consistent with the theory developed here, we propose new experimental measures that can serve to test the present theoretical framework. Finally, the influence of underlying symmetries of the dynamics on the nature of the gait patterns and their stability is analyzed. For example, breaking of a front-hind symmetry can lead to a change from absolute to relative co-ordination in the sense of von Holst (1939, Ergebnisse der Physiologie 42, 228). Also, differential stability of straight and reverse gaits results from thus lowering the symmetry.

Gait↗
PubMed1990

A dynamic theory of coordination of discrete movement.

The concepts of pattern dynamics and their adaptation through behavioral information, developed in the context of rhythmic movement coordination, are generalized to describe discrete movements of single components and the coordination of multiple components in discrete movement. In a first step we consider only one spatial component and study the temporal order inherent in discrete movement in terms of stable, reproducible space-time relationships. The coordination of discrete movement is captured in terms of relative timing. Using an exactly solvable nonlinear oscillator as a mathematical model, we show how the timing properties of discrete movement can be described by these pattern dynamics and discuss the relation of the pattern variables to observable end-effector movement. By coupling several such component dynamics in a fashion analogous to models of rhythmic movement coordination we capture the coordination of discrete movements of two components. We find the tendency to synchronize the component movements as the discrete analogon of in-phase locking and study its breakdown when the components become too different in their dynamic properties. The concept of temporal stability leads to the prediction that remote compensatory responses occur such as the restore synchronization when one component is perturbed. This prediction can be used to test the theory. We find that the discrete analogon to antiphase locking in rhythmic movement is a tendency to move sequentially, a finding that can also be subjected to empirical test.

Cybernetics↗
PubMed1989

Learning and recall in a dynamic theory of coordination patterns.

A dynamic theory of learning and recall of coordination patterns is developed in the context of relative timing skills. Characterizing the coordination patterns in such skills by the collective variable, relative phase, we choose a model system in which the intrinsic pattern dynamics as well as the influence of environmental and memorized information are well understood from previous experimental and theoretical work. To describe learning we endow memorized information with dynamics which is determined by a phenomenological strategy. Similarly, additional degrees of freedom must be introduced to understand recall. As such recall variables we choose the relative strengths with which each memorized pattern acts on the pattern dynamics and model their dynamics phenomenologically. The resulting dynamical system that resembles models used in pattern recognition theory is shown to adequately describe the learning and recall processes. Moreover, due to the operational character of the theory, several predictions emerge that are open to experimental test. In particular, we show under which conditions phase transitions occur in the dynamics of the coordination patterns during learning and during recall. Considering different time scales and their relations we demonstrate how these phase transitions can be identified and observed. Other predictions include the influence of the intrinsic pattern dynamics on the recall process and the existence of history and hysteresis effects in recall. We discuss different forms of "forgetting" and differentiation of memorized information. The results show how a new theoretical view of learning and recall as change of behavioral dynamics can lead to a different understanding of these processes by providing testable predictions.

Extremities↗
PubMed1988

Dynamic pattern generation in behavioral and neural systems.

In the search for principles of pattern generation in complex biological systems, an operational approach is presented that embraces both theory and experiment. The central mathematical concepts of self-organization in nonequilibrium systems (including order parameter dynamics, stability, fluctuations, and time scales) are used to show how a large number of empirically observed features of temporal patterns can be mapped onto simple low-dimensional (stochastic, nonlinear) dynamical laws that are derivable from lower levels of description. The theoretical framework provides a language and a strategy, accompanied by new observables, that may afford an understanding of dynamic patterns at several scales of analysis (including behavioral patterns, neural networks, and individual neurons) and the linkage among them.

Animals↗
PubMed1988

A synergetic theory of environmentally-specified and learned patterns of movement coordination. I. Relative phase dynamics.

This paper outlines and applies a synergetic strategy to the coordination of human rhythmical movement. It extends earlier empirical and theoretical work to include the influence of specific environmental information and of memory on the dynamics of the collective variables (order parameters) that characterize the coordination patterns. Key ideas concern cooperative and competitive influences on the collective dynamics. Recent experiments on environmentally specified and learned rhythmic movement patterns are modeled explicitly on the level of the collective variable, relative phase. New predictions are presented and research directions proposed that follow directly from the present theoretical approach.

Animals↗
PubMed1988

A synergetic theory of environmentally-specified and learned patterns of movement coordination. II. Component oscillator dynamics.

Rhythmic movement patterns have served as a model case for developing a synergetic theory of biological coordination. In part I of this work we extended the approach to environmentally-specified and learned movement patterns on the level of the collective variable relative phase. Here we show that an identical strategy may be applied to the same problem at the level of the component oscillators. Coordinative patterns and their dynamics are derived from the coupled component dynamics and their interaction with the environment. Thus, behavioral patterns are shown to arise in a purely self-organized fashion. New directions for further research (e.g. dynamics of action-perception systems) follow from the oscillator theory. Finally the relationship between our approach and other kinds of analyses of temporal order (e.g. phase resetting) is addressed.

Animals↗
PubMed1987

Space-time behavior of single and bimanual rhythmical movements: data and limit cycle model.

How do space and time relate in rhythmical tasks that require the limbs to move singly or together in various modes of coordination? And what kind of minimal theoretical model could account for the observed data? Earlier findings for human cyclical movements were consistent with a nonlinear, limit cycle oscillator model (Kelso, Holt, Rubin, & Kugler, 1981) although no detailed modeling was performed at that time. In the present study, kinematic data were sampled at 200 samples/second, and a detailed analysis of movement amplitude, frequency, peak velocity, and relative phase (for the bimanual modes, in phase and antiphase) was performed. As frequency was scaled from 1 to 6 Hz (in steps of 1 Hz) using a pacing metronome, amplitude dropped inversely and peak velocity increased. Within a frequency condition, the movement's amplitude scaled directly with its peak velocity. These diverse kinematic behaviors were modeled explicitly in terms of low-dimensional (nonlinear) dissipative dynamics, with linear stiffness as the only control parameter. Data and model are shown to compare favorably. The abstract, dynamical model offers a unified treatment of a number of fundamental aspects of movement coordination and control.

Functional Laterality↗
PubMed1986

A stochastic theory of phase transitions in human hand movement.

The order parameter equation for the relative phase of correlated hand movements, derived in a previous paper by Haken et al. (1985), is extended to a time-dependent stochastic differential equation. Its solutions are determined close to stationary points and for the transition region. Remarkably good agreement between this theory and recent experiments done by Kelso and Scholz (1985) is found, and new predictions are offered.

Hand↗