A simple algorithm to generate firing times for leaky integrate-and-fire neuronal model

  • Received: 01 December 2012 Accepted: 29 June 2018 Published: 01 September 2013
  • MSC : Primary: 60J60; Secondary: 60H35.

  • A method to generate first passage times for a class of stochastic processes is proposed. It does not require construction of the trajectories as usually needed in simulation studies, but is based on an integral equation whose unknown quantity is the probability density function of the studied first passage times and on the application of the hazard rate method. The proposed procedure is particularly efficient in the case of the Ornstein-Uhlenbeck process, which is important for modeling spiking neuronal activity.

    Citation: Aniello Buonocore, Luigia Caputo, Enrica Pirozzi, Maria Francesca Carfora. A simple algorithm to generate firing times for leaky integrate-and-fire neuronal model[J]. Mathematical Biosciences and Engineering, 2014, 11(1): 1-10. doi: 10.3934/mbe.2014.11.1

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  • A method to generate first passage times for a class of stochastic processes is proposed. It does not require construction of the trajectories as usually needed in simulation studies, but is based on an integral equation whose unknown quantity is the probability density function of the studied first passage times and on the application of the hazard rate method. The proposed procedure is particularly efficient in the case of the Ornstein-Uhlenbeck process, which is important for modeling spiking neuronal activity.


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  • This article has been cited by:

    1. Massimiliano Tamborrino, 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, 2016, 13, 1551-0018, 613, 10.3934/mbe.2016011
    2. Aniello Buonocore, Luigia Caputo, Enrica Pirozzi, Maria Francesca Carfora, A leaky integrate-and-fire model with adaptation for the generation of a spike train, 2016, 13, 1551-0018, 483, 10.3934/mbe.2016002
    3. M. F. Carfora, 2023, Chapter 8, 978-3-031-33049-0, 137, 10.1007/978-3-031-33050-6_8
    4. Luigia Caputo, Maria Francesca Carfora, Enrica Pirozzi, 2025, Chapter 21, 978-3-031-83887-3, 228, 10.1007/978-3-031-83885-9_21
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