Dynamics of Retrieval Process in Coupled Oscillator Models with Scattered Natural Frequency

Abstract

In this study, we consider the dynamics of the retrieval process in oscillator associative memory models that have frustrations and a distributed natural frequency. By applying the adiabatic approximation to a continuous-time model, we propose a corresponding discrete-time model. We derive maps of order parameters for the discrete-time model, in which the temporal correlations of noise with previous time steps are considered. It is found that the discrete-time model describes the behaviors of the continuous-time model well and that the fourth-order approximation in the map of order parameters is necessary for sufficient agreement with simulation results. The reason for the gaps between simulation results and theoretical results and the limitations of our theory are discussed.