A Spectral Analysis of the Sequence of Firing Phases in Stochastic Integrate-and-Fire Oscillators

Details A Spectral Analysis of the Sequence of Firing Phases in Stochastic Integrate-and-Fire Oscillators A Spectral Analysis of the Sequence of Firing Phases in Stochastic Integrate-and-Fire Oscillators

2009-07-21

arxiv.org/abs/0907.3700v1

Mathematics

Probability

1 zip file, 13 figures + .tex document + style and class files needed for compiling

Scientific paper

Integrate and fire oscillators are widely used to model the generation of action potentials in neurons. In this paper, we discuss small noise asymptotic results for a class of stochastic integrate and fire oscillators (SIFs) in which the buildup of membrane potential in the neuron is governed by a Gaussian diffusion process. To analyze this model, we study the asymptotic behavior of the spectrum of the firing phase transition operator. We begin by proving strong versions of a law of large numbers and central limit theorem for the first passage-time of the underlying diffusion process across a general time dependent boundary. Using these results, we obtain asymptotic approximations of the transition operator's eigenvalues. We also discuss connections between our results and earlier numerical investigations of SIFs.

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