We use mathematical analysis and numerical simulations to study the effects of recurrent synaptic connections in neural networks. These recurrent effects can be analyzed by expanding a spike probability function about the membrane potential in the absence of connections. This expansion can be written as a series of loops representing the recurrent signal transmission. Conditions for convergence of the series reveal the number of loops that are significant for the system's dynamics. This method is applied to a pair of mutually coupled spiking neurons to show how the membrane potential and cross-correlation function is changed by recurrence.
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