Dynamics of neural networks with a central element.

A neural network is considered which is designed as a system of phase oscillators and contains a central oscillator that interacts with a number of peripheral oscillators. Analytical and simulation methods are used to study the dynamics of the system that is conditioned by the interaction parameters and natural frequencies of the oscillators. The boundaries of parameter regions are found that correspond to the synchronization of the whole network or to partial synchronization between the central oscillator and a group of peripheral oscillators. For a system with two peripheral oscillators the bifurcation analysis is applied to describe the changes of synchronization modes. The implications of the results for attention modeling are discussed.

The synchronization principle in modelling of binding and attention.

The paper presents some mathematical models in support of the hypothesis that there is a general principle of information processing at the levels of both preattention and attention. It is claimed that at both levels, information processing is based on the coherent (synchronous) activity of neurons, neural populations, and brain structures. The difference between the two levels is presumed to relate to how synchronization is realized. At the level of preattention, synchronization results from the self-organization of the cortical activity, while at the level of attention, synchronous activity is controlled by special structures that act as a central executive. Two types of oscillatory neural networks are developed to model preattention and attention phenomena. In the preattention modelling, we concentrate on the binding problem. To solve this problem, a two-layer network of neural oscillators is developed. The network is able to generate two-frequency envelope oscillations, in which the amplitude of high-frequency oscillations is modulated by a lower frequency. This network synchronizes regions of oscillatory activity at high and low frequencies according to the type of stimulation. Such a synchronization gives feature binding for both simple and complex stimuli. Networks of phase oscillators with a central element are used to described different dynamic behaviour associated with the attention focus formation and switching. For the input to the attention system represented by two stimuli, we give a complete description of conditions when a specific attention focus can be formed. The results are interpreted and discussed in terms of attention modelling. This includes the interpretation of psychological experiments on visual selective attention, the problem of attention focus formation and the possibility of spontaneous attention switching .