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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Biological cybernetics 71 (1994), S. 177-185 
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract. A neural network model is considered which is designed as a system of phase oscillators and contains the central oscillator and peripheral oscillators which interact via the central oscillator. The regime of partial synchronization was studied when current frequencies of the central oscillator and one group of peripheral oscillators are near to each other while current frequencies of other peripheral oscillators are far from being synchronized with the central oscillator. Approximation formulas for the average frequency of the central oscillator in the regime of partial synchronization are derived, and results of computation experiments are presented which characterize the accuracy of the approximation.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Biological cybernetics 71 (1994), S. 177-185 
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract A neural network model is considered which is designed as a system of phase oscillators and contains the central oscillator and peripheral oscillators which interact via the central oscillator. The regime of partial synchronization was studied when current frequencies of the central oscillator and one group of peripheral oscillators are near to each other while current frequencies of other peripheral oscillators are far from being synchronized with the central oscillator. Approximation formulas for the average frequency of the central oscillator in the regime of partial synchronization are derived, and results of computation experiments are presented which characterize the accuracy of the approximation.
    Type of Medium: Electronic Resource
    Location Call Number Limitation Availability
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  • 3
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In this paper we present an oscillatory neural network composed of two coupled neural oscillators of the Wilson-Cowan type. Each of the oscillators describes the dynamics of average activities of excitatory and inhibitory populations of neurons. The network serves as a model for several possible network architectures. We study how the type and the strength of the connections between the oscillators affect the dynamics of the neural network. We investigate, separately from each other, four possible connection types (excitatory→excitatory, excitatory→inhibitory, inhibitory→excitatory, and inhibitory→inhibitory) and compute the corresponding bifurcation diagrams. In case of weak connections (small strength), the connection of populations of different types lead to periodicin-phase oscillations, while the connection of populations of the same type lead to periodicanti-phase oscillations. For intermediate connection strengths, the networks can enter quasiperiodic or chaotic regimes, and can also exhibit multistability. More generally, our analysis highlights the great diversity of the response of neural networks to a change of the connection strength, for different connection architectures. In the discussion, we address in particular the problem of information coding in the brain using quasiperiodic and chaotic oscillations. In modeling low levels of information processing, we propose that feature binding should be sought as a temporally coherent phase-locking of neural activity. This phase-locking is provided by one or more interacting convergent zones and does not require a central “top level” subcortical circuit (e.g. the septo-hippocampal system). We build a two layer model to show that although the application of a complex stimulus usually leads to different convergent zones with high frequency oscillations, it is nevertheless possible to synchronize these oscillations at a lower frequency level using envelope oscillations. This is interpreted as a feature binding of a complex stimulus.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Biological cybernetics 66 (1992), S. 319-325 
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract This paper describes the analysis of the well known neural network model by Wilson and Cowan. The neural network is modeled by a system of two ordinary differential equations that describe the evolution of average activities of excitatory and inhibitory populations of neurons. We analyze the dependence of the model's behavior on two parameters. The parameter plane is partitioned into regions of equivalent behavior bounded by bifurcation curves, and the representative phase diagram is constructed for each region. This allows us to describe qualitatively the behavior of the model in each region and to predict changes in the model dynamics as parameters are varied. In particular, we show that for some parameter values the system can exhibit long-period oscillations. A new type of dynamical behavior is also found when the system settles down either to a stationary state or to a limit cycle depending on the initial point.
    Type of Medium: Electronic Resource
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