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A Semi-Markov Leaky Integrate-and-Fire Model

Author

Listed:
  • Giacomo Ascione

    (Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”, Università degli Studi di Napoli Federico II, I-80126 Naples, Italy
    These authors contributed equally to this work.)

  • Bruno Toaldo

    (Dipartimento di Matematica “Giuseppe Peano”, Università degli Studi di Torino, 10123 Torino, Italy
    These authors contributed equally to this work.)

Abstract

In this paper, a Leaky Integrate-and-Fire (LIF) model for the membrane potential of a neuron is considered, in case the potential process is a semi-Markov process. Semi-Markov property is obtained here by means of the time-change of a Gauss-Markov process. This model has some merits, including heavy-tailed distribution of the waiting times between spikes. This and other properties of the process, such as the mean, variance and autocovariance, are discussed.

Suggested Citation

  • Giacomo Ascione & Bruno Toaldo, 2019. "A Semi-Markov Leaky Integrate-and-Fire Model," Mathematics, MDPI, vol. 7(11), pages 1-24, October.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:11:p:1022-:d:281238
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    References listed on IDEAS

    as
    1. Dexter O. Cahoy & Federico Polito & Vir Phoha, 2015. "Transient Behavior of Fractional Queues and Related Processes," Methodology and Computing in Applied Probability, Springer, vol. 17(3), pages 739-759, September.
    2. Erhan Cinlar, 1974. "Markov Additive Processes and Semi-Regeneration," Discussion Papers 118, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Meerschaert, Mark M. & Toaldo, Bruno, 2019. "Relaxation patterns and semi-Markov dynamics," Stochastic Processes and their Applications, Elsevier, vol. 129(8), pages 2850-2879.
    4. Yasuhiro Tsubo & Yoshikazu Isomura & Tomoki Fukai, 2012. "Power-Law Inter-Spike Interval Distributions Infer a Conditional Maximization of Entropy in Cortical Neurons," PLOS Computational Biology, Public Library of Science, vol. 8(4), pages 1-11, April.
    5. Aniello Buonocore & Luigia Caputo & Enrica Pirozzi & Luigi M. Ricciardi, 2011. "The First Passage Time Problem for Gauss-Diffusion Processes: Algorithmic Approaches and Applications to LIF Neuronal Model," Methodology and Computing in Applied Probability, Springer, vol. 13(1), pages 29-57, March.
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    Cited by:

    1. Lansky, Petr & Polito, Federico & Sacerdote, Laura, 2023. "Input-output consistency in integrate and fire interconnected neurons," Applied Mathematics and Computation, Elsevier, vol. 440(C).
    2. Enrica Pirozzi, 2024. "Mittag–Leffler Fractional Stochastic Integrals and Processes with Applications," Mathematics, MDPI, vol. 12(19), pages 1-20, October.

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