A Green's function approach to analysing the effects of random synaptic background activity in a model neural network

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Abstract
The effect of randomly distributed synaptic background activity on the states of self-sustained firing in a model neural network with shunting is investigated. Using mean field theory, the steady state of the network is expressed in terms of an ensemble-averaged single-neuron Green's function. This Green's function is shown to satisfy a matrix equation identical in form to that found in the tight-binding-alloy model of excitations on a one-dimensional disordered lattice. The ensemble averaging is then performed using a coherent potential approximation thus allowing the steady-state firing rate of the network to be determined. The firing rate is found to decrease as the mean level of background activity across the network is increased; a uniform background (zero variance) leads to a greater reduction than a randomly distributed one (non-zero variance).