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  • 1
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Annals of the New York Academy of Sciences 231 (1974), S. 0 
    ISSN: 1749-6632
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Natural Sciences in General
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Annals of the New York Academy of Sciences 357 (1980), S. 0 
    ISSN: 1749-6632
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Natural Sciences in General
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Journal of computational neuroscience 1 (1994), S. 69-87 
    ISSN: 1573-6873
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Medicine , Physics
    Notes: Abstract We describe four different mechanisms that lead to oscillations in a network of two reciprocally inhibitory cells. In two cases (intrinsic release and intrinsic escape) the frequency of the network oscillation is insensitive to the threshold voltage of the synaptic potentials. In the other two cases (synaptic release and synaptic escape) the network frequency is strongly determined by the threshold voltage of the synaptic connections. The distinction between the different mechanisms blurs as the function describing synaptic activation becomes less steep and as the model neurons are removed from the relaxation regime. These mechanisms provide insight into the parameters that control network frequency in motor systems that depend on reciprocal inhibition.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Journal of computational neuroscience 4 (1997), S. 151-160 
    ISSN: 1573-6873
    Keywords: locomotion ; central pattern generator ; oscillators ; mathematical models ; crayfish swimmerets
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Medicine , Physics
    Notes: Abstract Rhythmic movements of crayfish swimmerets are coordinated by a neural circuit that links their four abdominal ganglia. Each swimmeret is driven by its own small local circuit, or pattern-generating module. We modeled this networkas a chain of four oscillators, bidirectionally coupled to their nearest neighbors, and tested the model‘s ability to reproduce experimentally observed changes in intersegmental phases and in period caused by differential excitation of selected abdominal ganglia. The choices needed to match the experimental data lead to the followingpredictions: coupling between ganglia is asymmetric; the ascending and descending coupling have approximately equal strengths; intersegmental coupling does not significantly affect the frequency of the system; and excitation affects the intrinsic frequencies of the oscillators and might also change properties ofintersegmental coupling.
    Type of Medium: Electronic Resource
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  • 5
    ISSN: 1573-6873
    Keywords: gamma oscillations ; hippocampus ; interneurons
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Medicine , Physics
    Notes: Abstract We study some mechanisms responsible for synchronous oscillations and loss of synchrony at physiologically relevant frequencies (10–200 Hz) in a network of heterogeneous inhibitory neurons. We focus on the factors that determine the level of synchrony and frequency of the network response, as well as the effects of mild heterogeneity on network dynamics. With mild heterogeneity, synchrony is never perfect and is relatively fragile. In addition, the effects of inhibition are more complex in mildly heterogeneous networks than in homogeneous ones. In the former, synchrony is broken in two distinct ways, depending on the ratio of the synaptic decay time to the period of repetitive action potentials (τs/T), where T can be determined either from the network or from a single, self-inhibiting neuron. With τs/T 〉 2, corresponding to large applied current, small synaptic strength or large synaptic decay time, the effects of inhibition are largely tonic and heterogeneous neurons spike relatively independently. With τs/T 〈 1, synchrony breaks when faster cells begin to suppress their less excitable neighbors; cells that fire remain nearly synchronous. We show numerically that the behavior of mildly heterogeneous networks can be related to the behavior of single, self-inhibiting cells, which can be studied analytically.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Journal of computational neuroscience 5 (1998), S. 407-420 
    ISSN: 1573-6873
    Keywords: gamma oscillations ; hippocampus ; interneurons ; synchronization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Medicine , Physics
    Notes: Abstract We analyze the control of frequency for a synchronized inhibitory neuronal network. The analysis is done for a reduced membrane model with a biophysically based synaptic influence. We argue that such a reduced model can quantitatively capture the frequency behavior of a larger class of neuronal models. We show that in different parameter regimes, the network frequency depends in different ways on the intrinsic and synaptic time constants. Only in one portion of the parameter space, called phasic, is the network period proportional to the synaptic decay time. These results are discussed in connection with previous work of the authors, which showed that for mildly heterogeneous networks, the synchrony breaks down, but coherence is preserved much more for systems in the phasic regime than in the other regimes. These results imply that for mildly heterogeneous networks, the existence of a coherent rhythm implies a linear dependence of the network period on synaptic decay time and a much weaker dependence on the drive to the cells. We give experimental evidence for this conclusion.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Journal of computational neuroscience 9 (2000), S. 271-291 
    ISSN: 1573-6873
    Keywords: rhythms ; synchrony ; cortex ; alpha ; attention
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Medicine , Physics
    Notes: Abstract Neocortical networks of excitatory and inhibitory neurons can display alpha(α)-frequency rhythms when an animal is in a resting or unfocused state. Unlike some γ- and β-frequency rhythms, experimental observations in cats have shown that these α-frequency rhythms need not synchronize over long cortical distances. Here, we develop a network model of synaptically coupled excitatory and inhibitory cells to study this asynchrony. The cells of the local circuit are modeled on the neurons found in layer V of the neocortex where α-frequency rhythms are thought to originate. Cortical distance is represented by a pair of local circuits coupled with a delay in synaptic propagation. Mathematical analysis of this model reveals that the h and T currents present in layer V pyramidal (excitatory) cells not only produce and regulate the α-frequency rhythm but also lead to the occurrence of spatial asynchrony. In particular, these inward currents cause excitation and inhibition to have nonintuitive effects in the network, with excitation delaying and inhibition advancing the firing time of cells; these reversed effects create the asynchrony. Moreover, increased excitatory to excitatory connections can lead to further desynchronization. However, the local rhythms have the property that, in the absence of excitatory to excitatory connections, if the participating cells are brought close to synchrony (for example, by common input), they will remain close to synchrony for a substantial time.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Biological cybernetics 68 (1993), S. 393-407 
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract Synchronization properties of locally coupled neural oscillators were investigated analytically and by computer simulation. When coupled in a manner that mimics excitatory chemical synapses, oscillators having more than one time scale (relaxation oscillators) are shown to approach synchrony using mechanisms very different from that of oscillators with a more sinusoidal waveform. The relaxation oscillators make critical use of fast modulations of their thresholds, leading to a rate of synchronization relatively independent of coupling strength within some basin of attraction; this rate is faster for oscillators that have conductance-based features than for neural caricatures such as the FitzHugh-Nagumo equations that lack such features. Computer simulations of one-dimensional arrays show that oscillators in the relaxation regime synchronize much more rapidly than oscillators with the same equations whose parameters have been modulated to yield a more sinusoidal waveform. We present a heuristic explanation of this effect based on properties of the coupling mechanisms that can affect the way the synchronization scales with array length. These results suggest that the emergent synchronization behavior of oscillating neural networks can be dramatically influenced by the intrinsic properties of the network components. Possible implications for perceptual feature binding and attention are discussed.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Journal of mathematical biology 38 (1999), S. 479-533 
    ISSN: 1432-1416
    Keywords: Keywords: Central pattern generator ; Relative coordination ; Oscillation ; Singular perturbation ; Subharmonics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract.  We discuss a method by which the dynamics of a network of neurons, coupled by mutual inhibition, can be reduced to a one-dimensional map. This network consists of a pair of neurons, one of which is an endogenous burster, and the other excitable but not bursting in the absence of phasic input. The latter cell has more than one slow process. The reduction uses the standard separation of slow/fast processes; it also uses information about how the dynamics on the slow manifold evolve after a finite amount of slow time. From this reduction we obtain a one-dimensional map dependent on the parameters of the original biophysical equations. In some parameter regimes, one can deduce that the original equations have solutions in which the active phase of the originally excitable cell is constant from burst to burst, while in other parameter regimes it is not. The existence or absence of this kind of regulation corresponds to qualitatively different dynamics in the one-dimensional map. The computations associated with the reduction and the analysis of the dynamics includes the use of coordinates that parameterize by time along trajectories, and “singular Poincaré maps” that combine information about flows along a slow manifold with information about jumps between branches of the slow manifold.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Journal of mathematical biology 33 (1995), S. 261-280 
    ISSN: 1432-1416
    Keywords: Neural oscillator ; Pulse coupling ; Bistability ; Synaptic coupling ; Van der Pol oscillator
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Relaxation oscillators interacting via models of excitatory chemical synapses with sharp thresholds can have stable anti-phase as well as in-phase solutions. The mechanism for anti-phase demonstrated in this paper relies on the fact that, in a large class of neural models, excitatory input slows down the receiving oscillator over a portion of its trajectory. We analyze the effect of this “virtual delay” in an abstract model, and then show that the hypotheses of that model hold for widely used descriptions of bursting neurons.
    Type of Medium: Electronic Resource
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