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We present a first-order non-homogeneous Markov model for theinterspike-interval density of a continuously stimulated spiking neuron. Themodel allows the conditional interspike-interval density and the stationaryinterspike-interval density to be expressed as products of two separatefunctions, one of which describes only the neuron characteristics, and theother of which describes only the signal characteristics. This allows the useof this model to predict the response when the underlying neuron model is notknown or well determined. The approximation shows particularly clearly thatsignal autocorrelations and cross-correlations arise as natural features of theinterspike-interval density, and are particularly clear for small signals andmoderate noise. We show that this model simplifies the design of spiking neuroncross-correlation systems, and describe a four-neuron mutual inhibition networkthat generates a cross-correlation output for two input signals.

A First-Order Non-Homogeneous Markov Model for the Response of Spiking Neurons Stimulated by Small Phase-Continuous Signals