The Cauchy problem for one-dimensional spiking neuron models.
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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 [Formula: see text] 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.
SUBMITTER: Brette R
PROVIDER: S-EPMC2289251 | biostudies-other | 2008 Mar
REPOSITORIES: biostudies-other
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