Mathematical Biosciences and Engineering, 2014, 11(1): 1-10. doi: 10.3934/mbe.2014.11.1.

Primary: 60J60; Secondary: 60H35.

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

1. Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Via Cintia, Napoli
2. Istituto per le Appplicazioni del Calcolo "Mauro Picone", Consiglio Nazionale delle Ricerche, Via Pietro Castellino, Napoli

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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Keywords spike train generation; Ornstein-Uhlenbeck process; first passage time; hazard rate method.; instantaneous firing rate

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

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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, Mathematical Biosciences and Engineering, 2016, 13, 3, 613, 10.3934/mbe.2016011
  • 2. Maria Francesca Carfora, Enrica Pirozzi, Luigia Caputo, Aniello Buonocore, A leaky integrate-and-fire model with adaptation for the generation of a spike train, Mathematical Biosciences and Engineering, 2016, 13, 3, 483, 10.3934/mbe.2016002

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Copyright Info: 2014, Aniello Buonocore, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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