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  • 1
    Electronic Resource
    Electronic Resource
    Synchronized oscillations in the visual cortex — a synergetic model (1996)
    Springer
    Biological cybernetics 74 (1996), S. 31-39 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract We present an oscillator network model for the synchronization of oscillatory neuronal activity underlying visual processing. The single neuron is modeled by means of a limit cycle oscillator with an eigenfrequency corresponding to visual stimulation. The eigenfrequency may be time dependent. The mutual coupling strengths are unsymmetrical and activity dependent, and they scatter within the network. Synchronized clusters (groups) of neurons emerge in the network due to the visual stimulation. The different clusters correspond to different visual stimuli. There is no limitation of the number of stimuli. Distinct clusters do not perturb each other, although the coupling strength between all model neurons is of the same order of magnitude. Our analysis is not restricted to weak coupling strength. The scatter of the couplings causes shifts of the cluster frequencies. The model's behavior is compared with the experimental findings. The coupling mechanism is extended in order to model the influence of bicucullin upon the neural network. We additionally investigate repulsive couplings, which lead to constant phase differences between clusters of the same frequency. Finally, we consider the problem of selective attention from the viewpoint of our model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00199135
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Synchronized oscillations in the visual cortex – a synergetic model (1995)
    Springer
    Biological cybernetics 74 (1995), S. 31-39 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract.  We present an oscillator network model for the synchronization of oscillatory neuronal activity underlying visual processing. The single neuron is modeled by means of a limit cycle oscillator with an eigenfrequency corresponding to visual stimulation. The eigenfrequency may be time dependent. The mutual coupling strengths are unsymmetrical and activity dependent, and they scatter within the network. Synchronized clusters (groups) of neurons emerge in the network due to the visual stimulation. The different clusters correspond to different visual stimuli. There is no limitation of the number of stimuli. Distinct clusters do not perturb each other, although the coupling strength between all model neurons is of the same order of magnitude. Our analysis is not restricted to weak coupling strength. The scatter of the couplings causes shifts of the cluster frequencies. The model’s behavior is compared with the experimental findings. The coupling mechanism is extended in order to model the influence of bicucullin upon the neural network. We additionally investigate repulsive couplings, which lead to constant phase differences between clusters of the same frequency. Finally, we consider the problem of selective attention from the viewpoint of our model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004220050216
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    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Cortical pattern formation during visual hallucinations (1995)
    Springer
    Journal of biological physics 21 (1995), S. 177-210 
    Details
    ISSN: 1573-0689
    Keywords: activator-inhibitor network ; pattern formation ; bifurcation ; center manifold ; reduced problem ; slaving principle ; order parameter equation ; phase diffusion ; visual hallucinations ; epilepsy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Physics
    Notes: Abstract We theoretically investigate pattern formation during simple visual hallucinations caused by epileptic activity. To this end we analyze the activator-inhibitor model of Ermentrout and Cowan [1]. In contrast to these authors we focus on a different disease mechanism: According to experimental findings (cf. [2]) we decrease the influence of the inhibitor on the activator. This causes spontaneous pattern formation due to a bifurcation. The model parameters determine whether one or two or four modes become unstable. By means of the center manifold theorem, in all cases the order parameter equation is derived, the stability of the solution is proofed, and the bifurcating activity pattern is calculated explicitely in lowest order. Taking into account terms up to third order in all cases the order parameter equation has a potential. For the two-modes and the four-modes instability this potential causes a winner-takes all dynamics. We integrate the order parameter equation numerically and plot the visual hallucinations which result from the bifurcating cortical activity. The theoretically derived hallucinations correspond to clinically observed visual hallucinations (cf. [3, 4]), which are, for instance, well-known from petit mal epilepsy [5]. Finally we investigate the influence of noise on the activity patterns as well as the visual hallucinations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00712345
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Resetting biological oscillators—A stochastic approach (1996)
    Springer
    Journal of biological physics 22 (1996), S. 27-64 
    Details
    ISSN: 1573-0689
    Keywords: phase-resetting ; phase singularity ; black hole ; Fokker-Planck equation ; Langevin equation ; synchronization ; stimulation ; tremor
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Physics
    Notes: Abstract We present a stochastic approach to phase-resetting of an ensemble of oscillators. In order to describe stimulation-induced dynamical phenomena we develop a stochastic model which consists of an ensemble of phase oscillators interacting via random forces. Every single oscillator is submitted to a phase stimulus. The ensemble's dynamics is determined by a Fokker-Planck equation. The stationary states are calculated explicitly, whereas the transients are analysed numerically. If the stimulus of a given (non-vanishing) intensity is administered at a critical initial cluster phase for a critical duration T crit the ensemble's synchronized oscillation is annihilated. A transition from type 1 resetting to type 0 resetting occurs when the stimulation duration exceeds T crit. Stimulation causes a shift of the mean frequency of every single oscillator. This frequency shift is explicitly calculated by deriving the mean first passage time. The model shows that there is a subcritical intensity which is connected with an enhanced vulnerability to stimulation. The desynchronized states, the so-called black holes, are typically associated with a double peak in the ensemble's phase distribution. This is important for analysing experimental data because simple peak-detection algorithms are not able to extract the underlying dynamics. Our results are discussed from the experimentator's point of view so that the insights derived from our model can improve data analysis and design of stimulation experiments.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00383820
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  • 5
    Electronic Resource
    Electronic Resource
    A theoretical model of sinusoidal forearm tracking with delayed visual feedback (1995)
    Springer
    Journal of biological physics 21 (1995), S. 83-112 
    Details
    ISSN: 1573-0689
    Keywords: visual tracking ; delayed feedback ; differential-delay equations ; stability analysis ; instabilities ; nonlinear oscillations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Physics
    Notes: Abstract We present a phenomenological model to an experiment, where a person is systematically confronted with a delayed effect of her or his reaction to a time-periodic external signal. The model equations are derived from purely macroscopic considerations. Applying methods developed in the realm of synergetics we can analyze the first instability in the person's behaviour semi-analytically. A careful numerical study is devoted to the higher order instabilities and a comparison between experiment and the results obtained from our model is performed in detail.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00705593
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    Sscillatory Cortical Activity during Visual Hallucinations (1997)
    Springer
    Journal of biological physics 23 (1997), S. 21-66 
    Details
    ISSN: 1573-0689
    Keywords: Activator-inhibitor network ; Pattern formation ; Bifurcation ; Center manifold ; Order parameter equation ; Blinking rolls ; Visual hallucinations.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Physics
    Notes: Abstract From a theoretical point of view we investigate cortical activity patterns causing dynamic visual hallucinations. For this reason we analyze an oscillatory instability of the dynamics ofthe activator-inhibitor model of Ermentrout and Cowan.Such an oscillatory instability occurs as a result of several disease mechanisms.We explicitly derive the order parameter equation. By means of the averaging theorem, we obtain the averaged order parameter equation.The latter enables us to determine stable and unstable bifurcating cortical activity patterns analytically in lowest order.Depending on model parameters as well as on initial conditions two types of cortical activity patterns occur: travelling waves and ’blinking rolls‘, i.e.standing waves oscillating with the same frequency and with a phase shift of π/2. In contrast to cortical activitypatterns caused by non-oscillatory instabilitiesanalyzed by Ermentrout and Cowan and by the author the travelling waves and the blinking rolls lead to a variety of dynamic visual hallucinations which are discussed indetail.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004990707739
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    Paper (German National Licenses)
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  • 7
    Electronic Resource
    Electronic Resource
    Phase resetting associated with changes of burst shape (1996)
    Springer
    Journal of biological physics 22 (1996), S. 125-155 
    Details
    ISSN: 1573-0689
    Keywords: Phase resetting ; Phase singularity ; Black hole ; Fokker-Planck equation ; Langevin equation ; Synchronization ; Stimulation ; Tremor ; Burst splitting
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Physics
    Notes: Abstract Based on our stochastic approach to phase resetting of an ensemble of oscillators, in this article we investigate two stimulation mechanisms which exhibit qualitatively different dynamical behaviour as compared with the stimulation mechanism analysed in a previous study. Both the ‘old’ as well as one of the ‘new’ stimulation mechanisms give rise to a characteristic desynchronization behaviour: A stimulus of a given (non-vanishing) intensity administered at a critical initial ensemble phase for a critical duration T crit annihilates the ensemble's synchronized oscillation. When the stimulation duration exceeds T crit a transition from type 1 resetting to type 0 resetting occurs. The second ‘new’ stimulation mechanism does not cause a desynchronization which is connected with a phase singularity. Correspondingly this mechanism only leads to type 1 resetting. In contrast to the stimulation mechanism analysed in a previous study, both ‘new’ stimulation mechanisms cause burst splitting. According to our results, in this case peak or onset detection algorithms are not able to reveal a correct estimate of the ensemble phase. Thus, whenever stimulation induced burst splitting occurs, phase-resetting curves determined by means of peak or onset detection may be nothing but artifacts. Therefore it is necessary to understand burst splitting in order to develop reliable phase detection algorithms, which are e.g. based on detecting bursts' centers of mass. Our results are important for experimentalists: Burst splitting is, for instance, well-known from tremor resetting experiments. Thus, it often turned out to be at least rather difficult to derive reliable phase-resetting curves from experimental data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00417647
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    Paper (German National Licenses)
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