ASSOCIATIVE MEMORY-BASED ON SYNCHRONIZED FIRING OF SPIKING NEURONS WITH TIME-DELAYED INTERACTIONS

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.