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Mathematical Biosciences and Engineering

2014, Volume 11, Issue 2: 217-231. doi: 10.3934/mbe.2014.11.217
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On a spike train probability model with interacting neural units

  • 1.
    Dipartimento di Matematica, Università degli Studi di Salerno, Via Giovanni Paolo II, 132, I-84084 Fisciano (SA)
  • 2.
    Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Via Cintia, I-80126 Napoli
  • Received: 01 October 2012 Accepted: 29 June 2018 Published: 01 October 2013

  • MSC : Primary: 60J28, 92B20; Secondary: 60K20.

  • We investigate an extension of the spike train stochastic model based on the conditionalintensity, in which the recovery function includes an interaction between several excitatoryneural units. Such function is proposed as depending both on the time elapsed since thelast spike and on the last spiking unit. Our approach, being somewhat related to thecompeting risks model, allows to obtain the general form of the interspike distribution andof the probability of consecutive spikes from the same unit. Various results are finally presentedin the two cases when the free firing rate function (i) is constant, and (ii) has a sinusoidal form.

    Citation: Antonio Di Crescenzo, Maria Longobardi, Barbara Martinucci. On a spike train probability model with interacting neural units[J]. Mathematical Biosciences and Engineering, 2014, 11(2): 217-231. doi: 10.3934/mbe.2014.11.217

    Related Papers:

  • We investigate an extension of the spike train stochastic model based on the conditionalintensity, in which the recovery function includes an interaction between several excitatoryneural units. Such function is proposed as depending both on the time elapsed since thelast spike and on the last spiking unit. Our approach, being somewhat related to thecompeting risks model, allows to obtain the general form of the interspike distribution andof the probability of consecutive spikes from the same unit. Various results are finally presentedin the two cases when the free firing rate function (i) is constant, and (ii) has a sinusoidal form.


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  • © 2014 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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