Spike-timing-dependent plasticity for neurons with recurrent connections

The dynamics of the learning equation, which describes the evolution of the synaptic weights, is derived in the situation where the network contains recurrent connections. The derivation is carried out for the Poisson neuron model. The spiking-rates of the recurrently connected neurons and their cross-correlations are determined self- consistently as a function of the external synaptic inputs. The solution of the learning equation is illustrated by the analysis of the particular case in which there is no external synaptic input. The general learning equation and the fixed-point structure of its solutions is discussed.