Pattern coding based on firing times in a network of spiking neurons

We study two types of associative memory models incorporating the concept of temporal coding: a prototype oscillator neural network consisting of simple phase oscillators with distributed natural frequencies and a network of spiking neurons with time-delayed interactions. For the oscillator network, which is designed to encode the phase differences of the oscillators, obtaining the macroscopic order parameter equations to analyze phase diagrams for the storage capacity, we show that the occurrence of memory retrieval is ensured even in the presence of natural frequency distribution and white noise. For the network of spiking neurons with simple learning rule of Hebb type, we also show that successful retrieval accompanying synchronized firing of neurons of a target pattern is realized. In the low loading limit α=P/N=0 we can reduce an original dynamics of N degrees of freedom into that of a few degrees. In the case of an extensive number of stored patterns (a>0) we give an approximate analysis to explain the result of numerical simulations qualitatively