A new firing paradigm for integrate and fire stochastic neuronal models

Roberta Sirovich; Luisa  Testa

doi:10.3934/mbe.2016010

Article Contents

2016, Volume 13, Issue 3: 597-611. Doi: 10.3934/mbe.2016010

This issue Previous Article On the properties of input-to-output transformations in neuronal networks Next Article Approximation of the first passage time density of a Wiener process to an exponentially decaying boundary by two-piecewise linear threshold. Application to neuronal spiking activity

A new firing paradigm for integrate and fire stochastic neuronal models

Roberta Sirovich^1, and
Luisa Testa^2,

1.
Department of Mathematics "G. Peano", University of Torino, Via Carlo Alberto 10, 10123 Torino
2.
Department of Mathematics G. Peano, University of Torino, Via Carlo Alberto 10, 10123 - Torino

Received: April 30, 2015

Revised: September 30, 2015

Published: December 2015

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Abstract

A new definition of firing time is given in the framework of Integrate and Fire neuronal models. The classical absorption condition at the threshold is relaxed and the firing time is defined as the first time the membrane potential process lies above a fixed depolarisation level for a sufficiently long time. The mathematical properties of the new firing time are investigated both for the Perfect Integrator and the Leaky Integrator. In the latter case, a simulation study is presented to complete the analysis where analytical results are not yet achieved.

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Mathematics Subject Classification: 60J99, 92Bxx.

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