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Diffusion approximation and first passage time problem for a model neuron

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Abstract

A diffusion equation for the transition p.d.f. describing the time evolution of the membrane potential for a model neuron, subjected to a Poisson input, is obtained, without breaking up the continuity of the underlying random function. The transition p.d.f. is calculated in a closed form and the average firing interval is determined by using the steady-state limiting expression of the transition p.d.f. The Laplace transform of the first passage time p.d.f. is then obtained in terms of Parabolic Cylinder Functions as solution of a Weber equation, satisfying suitable boundary conditions. A continuous input model is finally investigated.

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Authors and Affiliations

  1. Laboratorio di Cibernetica del C.N.R. Arco Felice, Naples, Italy

    R. M. Capocelli

  2. Department of Theoretical Biology, University of Chicago, Chicago, Illinois, USA

    L. M. Ricciardi

  3. Laboratorio di Cibernetica del C.N.R. Arco Felice, Naples, Italy

    L. M. Ricciardi

Authors
  1. R. M. Capocelli
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  2. L. M. Ricciardi
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Capocelli, R.M., Ricciardi, L.M. Diffusion approximation and first passage time problem for a model neuron. Kybernetik 8, 214–223 (1971). https://doi.org/10.1007/BF00288750

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  • DOI: https://doi.org/10.1007/BF00288750

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