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On Fractional Stochastic Modeling of Neuronal Activity Including Memory Effects

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Computer Aided Systems Theory – EUROCAST 2017 (EUROCAST 2017)

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Abstract

In order to model the memory and to describe the memory effects in the firing activity of a single neuron subject to a time-dependent input current, a fractional stochastic Langevin-type equation is considered. Two different discretization formulas are derived and the corresponding algorithms are implemented by means of R-codes for several values of the parameters. Reset mechanisms after successive spike times are suitably imposed to compare simulation results. The firing rates and some neuronal statistical estimates obtained by means the two algorithms are provided and discussed.

This paper is partially supported by G.N.C.S.- INdAM.

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Via Cintia, 80126, Napoli, Italy

    Giacomo Ascione & Enrica Pirozzi

Authors
  1. Giacomo Ascione
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  2. Enrica Pirozzi
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Corresponding author

Correspondence to Enrica Pirozzi .

Editor information

Editors and Affiliations

  1. University of Las Palmas de Gran Canaria, Las Palmas de Gran Canaria, Spain

    Roberto Moreno-Díaz

  2. Johannes Kepler University Linz, Linz, Austria

    Franz Pichler

  3. University of Las Palmas de Gran Canaria, Las Palmas de Gran Canaria, Spain

    Alexis Quesada-Arencibia

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Ascione, G., Pirozzi, E. (2018). On Fractional Stochastic Modeling of Neuronal Activity Including Memory Effects. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2017. EUROCAST 2017. Lecture Notes in Computer Science(), vol 10672. Springer, Cham. https://doi.org/10.1007/978-3-319-74727-9_1

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  • DOI: https://doi.org/10.1007/978-3-319-74727-9_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-74726-2

  • Online ISBN: 978-3-319-74727-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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