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Mathematical Biosciences and Engineering

2016, Volume 13, Issue 3: 483-493. doi: 10.3934/mbe.2016002
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A leaky integrate-and-fire model with adaptation for the generation of a spike train

  • 1.
    Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli Federico II, Via Cintia, 80126 Napoli
  • 2.
    Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Via Cintia, Napoli
  • 3.
    Istituto per le Appplicazioni del Calcolo "Mauro Picone", Consiglio Nazionale delle Ricerche, Via Pietro Castellino, Napoli
  • Received: 01 April 2015 Accepted: 29 June 2018 Published: 01 January 2016

  • MSC : Primary: 60J60; Secondary: 60H35.

  • A model is proposed to describe the spike-frequency adaptation observed in many neuronal systems. We assume that adaptation is mainly due to a calcium-activated potassium current, and we consider two coupled stochastic differential equations for which an analytical approach combined with simulation techniques and numerical methods allow to obtain both qualitative and quantitative results about asymptotic mean firing rate, mean calcium concentration and the firing probability density. A related algorithm, based on the Hazard Rate Method, is also devised and described.

    Citation: Aniello Buonocore, Luigia Caputo, Enrica Pirozzi, Maria Francesca Carfora. A leaky integrate-and-fire model with adaptation for the generation of a spike train[J]. Mathematical Biosciences and Engineering, 2016, 13(3): 483-493. doi: 10.3934/mbe.2016002

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  • A model is proposed to describe the spike-frequency adaptation observed in many neuronal systems. We assume that adaptation is mainly due to a calcium-activated potassium current, and we consider two coupled stochastic differential equations for which an analytical approach combined with simulation techniques and numerical methods allow to obtain both qualitative and quantitative results about asymptotic mean firing rate, mean calcium concentration and the firing probability density. A related algorithm, based on the Hazard Rate Method, is also devised and described.


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  • © 2016 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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    沈阳化工大学材料科学与工程学院 沈阳 110142

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