Behaviors of Spike Output Jitter in the Integrate-and-Fire Model

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Abstract
We consider behaviors of output jitter in the simplest spiking model, the integrate-and-fire model. The full spectrum of behaviors is found: The output jitter is sensitive to the input distribution and can be a constant, diverge to infinity, or converge to zero. Exact formulas for the convergence or the divergence of output jitter are given. Our results suggest that the exponential distribution is the critical case: A faster rate of decrease in the distribution tail as compared to the exponential distribution tail ensures the convergence of output jitter, whereas slower decay in the distribution tail causes the divergence of output jitter.