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Open AccessArticle

A Semi-Markov Leaky Integrate-and-Fire Model

by Giacomo Ascione 1,*,† and Bruno Toaldo 2,†
1
Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”, Università degli Studi di Napoli Federico II, I-80126 Naples, Italy
2
Dipartimento di Matematica “Giuseppe Peano”, Università degli Studi di Torino, 10123 Torino, Italy
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2019, 7(11), 1022; https://doi.org/10.3390/math7111022
Received: 9 September 2019 / Revised: 22 October 2019 / Accepted: 24 October 2019 / Published: 29 October 2019
(This article belongs to the Special Issue Stochastic Processes in Neuronal Modeling)
In this paper, a Leaky Integrate-and-Fire (LIF) model for the membrane potential of a neuron is considered, in case the potential process is a semi-Markov process. Semi-Markov property is obtained here by means of the time-change of a Gauss-Markov process. This model has some merits, including heavy-tailed distribution of the waiting times between spikes. This and other properties of the process, such as the mean, variance and autocovariance, are discussed. View Full-Text
Keywords: Semi-Markov processes; LIF models; fractional equations Semi-Markov processes; LIF models; fractional equations
MDPI and ACS Style

Ascione, G.; Toaldo, B. A Semi-Markov Leaky Integrate-and-Fire Model. Mathematics 2019, 7, 1022.

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