Oscillator neural network model with distributed native frequencies

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Abstract

We study associative memory of an oscillator neural network with distributed native frequencies. The model is based on the use of the Hebb learning rule with random patterns (\(\xi_i^{\mu}=\pm 1\)), and the distribution function of native frequencies is assumed to be symmetric with respect to its average. Although the system with an extensive number of stored patterns is not allowed to get entirely synchronized, long time behaviors of the macroscopic order parameters describing partial synchronization phenomena can be obtained by discarding the contribution from the desynchronized part of the system. The oscillator network is shown to work as associative memory accompanied by synchronized oscillations. A phase diagram representing properties of memory retrieval is presented in terms of the parameters characterizing the native frequency distribution. Our analytical calculations based on the self-consistent signal-to-noise analysis are shown to be in excellent agreement with numerical simulations, confirming the validity of our theoretical treatment.

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Dynamics of neuronal interactions in monkey cortex in relation to behavioural events.

Y Prut, Nicholas H. Bergman, Aryeh M Abeles … (1995)

It is possible that brain cortical function is mediated by dynamic modulation of coherent firing in groups of neurons. Indeed, a correlation of firing between cortical neurons, seen following sensory stimuli or during motor behaviour, has been described. However, the time course of modifications of correlation in relation to behaviour was not evaluated systematically. Here we show that correlated firing between single neurons, recorded simultaneously in the frontal cortex of monkeys performing a behavioural task, evolves within a fraction of a second, and in systematic relation to behavioural events. Moreover, the dynamic patterns of correlation depend on the distance between neurons, and can emerge even without modulation of the firing rates. These findings support the notion that neurons can associate rapidly into a functional group in order to perform a computational task, at the same time becoming dissociated from concurrently activated competing groups. Thus, they call for a revision of prevailing models of neural coding that rely solely on single neuron firing rates.