Oscillator neural network model with distributed native frequencies

TL;DR

This paper investigates an oscillator neural network model with distributed native frequencies, demonstrating its ability to function as associative memory through synchronized oscillations and providing a phase diagram of its memory retrieval properties.

Contribution

It introduces an analytical framework for understanding associative memory in oscillator networks with distributed frequencies, validated by numerical simulations.

Findings

The network can store and retrieve patterns via synchronized oscillations.

A phase diagram characterizes memory retrieval based on frequency distribution parameters.

Analytical results agree well with numerical simulations.

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.