Dynamics of Order Parameters in Oscillator Associative Memory Models with Scattered Natural Frequency under External Noise

Abstract

In this study, we consider the dynamics of the order parameters in oscillator associative memory models with scattered natural frequency under external noise. We first study the stationary state of the continuous-time model. Based on this knowledge, by applying the adiabatic approximation and the ergodic hypothesis to the continuous-time model, we propose a discrete-time model. For the discrete-time model, we derive maps of order parameters by applying statistical neuro dynamics. When the external noise is large, the system cannot retrieve an imbedded pattern, and hence, the overlap becomes zero and variance of the crosstalk noise becomes small in the stationary state. We discuss the limitations of our theory and the reason for the gaps between simulation results and theoretical results.