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Journal Articles Cognitive Neurodynamics Year : 2008

The Cauchy problem for one-dimensional spiking neuron models

Romain Brette
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Abstract

I consider spiking neuron models defined by a one-dimensional differential equation and a reset—i.e., neuron models of the integrate-and-fire type. I address the question of the existence and uniqueness of a solution on $${\mathbb{R}}$$ for a given initial condition. It turns out that the reset introduces a countable and ordered set of backward solutions for a given initial condition. I discuss the implications of these mathematical results in terms of neural coding and spike timing precision.

Dates and versions

inria-00423347 , version 1 (09-10-2009)

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Romain Brette. The Cauchy problem for one-dimensional spiking neuron models. Cognitive Neurodynamics, 2008, 2, pp.21--27. ⟨10.1007/s11571-007-9032-y⟩. ⟨inria-00423347⟩
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