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Interaction between nerve cells, mediated by electrical coupling, is a common feature of the nervous system. When such electrical interactions occur within an entire population of similar neurons, the dynamic behavior of each individual cell is influenced by the properties of the whole network. It is shown that when the membrane impedance of such cells can be linearized to a satisfactory approximation and the zeros and poles of the linearized impedance are known, analytical solutions to the network equations can be found that describe the dynamics of the responses of any given cell to one-dimensional and two-dimensional stimuli. This analysis applied to the network of photoreceptors and horizontal cells in the vertebrate retina may be helpful in understanding the initial stages in the processing of visual information.