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We investigate the dynamics of a neural network where each neuron evolvesaccording to the combined effects of deterministic integrate-and-fire dynamicsand purely inhibitory coupling with K randomly-chosen "neighbors". Theinhibition reduces the voltage of a given neuron by an amount Delta when one ofits neighbors fires. The interplay between the integration and inhibition leadsto a steady state which is determined by solving the rate equations for theneuronal voltage distribution. We also study the evolution of a single neuronand find that the mean lifetime between firing events equals 1+K*Delta and thatthe probability that a neuron has not yet fired decays exponentially with time.Comment: 6 pages, 4 figures, 2-column format, to be submitted to PR

Steady state of an inhibitory neural network