M. Yoshioka et M. Shiino, ASSOCIATIVE MEMORY-BASED ON SYNCHRONIZED FIRING OF SPIKING NEURONS WITH TIME-DELAYED INTERACTIONS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 58(3), 1998, pp. 3628-3639
We study associative memory of a neural network of spiking neurons wit
h time-delayed synaptic interactions incorporating the time taken by a
n action potential to propagate along the axon. Individual spiking neu
rons are described by a set of nonlinear differential equations capabl
e of exhibiting excitability such as that of Hodgkin-Huxley and FitzHu
gh neurons. When a simple learning rule of the autocorrelation type ba
sed on random patterns is assumed, memory retrieval is shown to be acc
ompanied by synchronized firing of neurons. The reduced dynamics with
a few degrees of freedom of the network with a finite number of stored
patterns is analytically derived in the limit of infinitely many neur
ons. The dependence of the appearance of retrieval states on the distr
ibution of time delay and on the size of refractory period given impli
citly in the model is obtained, showing good agreement between the res
ult of numerical simulations and that obtained from the reduced dynami
cs. The behavior of the network with an extensive number of patterns i
s also investigated and an approximate analysis is presented to discus
s the storage capacity.